Aspects of Metaphor in Physics (Linguistische Arbeiten) 3484304073, 9783484304079

Table of contents :
Acknowledgements
Abbreviations
1. Introduction
Part One: The notion of metaphor and its relation to the discourse of physics
2. Approaches to metaphor: past and present
2.1. A short history of metaphor
2.2. Metaphor, an enemy of science: the early modern view
2.3. Metaphor, a friend of science: contemporary physicists on scientific language
2.4. Current paradigms in research on metaphor in science
3. Identifying metaphor in physical science: sorts, functions, and related concepts
3.1. Metaphor and related concepts
3.2. A working definition of metaphor
3.3. Sorts and functions of metaphor in physical discourse
Part Two: Metaphors in physics
4. Underlying metaphors of everyday thought in meta-theory and the concept formation of physics
4.1. Hypostasis
4.2. Spatial metaphor
4.3. Animism and anthropomorphism
5. World theories in meta-theory and the concept formation
5.1. The notions “world theory” and “world model”
5.2. World machine
5.3. The world as a text
6. Stipulative reference extension
6.1. Stipulation of meaning: Huygens’ notion of sound wave
6.2. Invisible light and Roentgen’s “invisible rays”
7. Assimilative metaphor
7.1. “Fluid” electricity
7.2. The concept of wave
7.3. Life stories of metaphor: from metaphorical to literal and literal to metaphorical
8. Theory-constitutive and educational metaphors
8.1. Constitutive metaphor: waves of probability
8.2. Educational metaphor: curvature of space
8.3. From explanation to rhetoric
9. Metaphor and style: “figures of speech” in the language of physics
9.1. The position of “figures of speech” in the discourse of physics
9.2. The arrow of time
9.3. Heat death
9.4. Maxwell’s demon
10. Transfer of denotations in the terminology of physics
10.1. Metaphors in general language and in the terminology of physics: the general language basis for the transfer of denotations
10.2. Types of transfer of denotations
10.3. The terminology of physics and related disciplines
10.4. Fantasy-metaphor: the case of particle physics
10.5. “Mechanical work”: underlying metaphor, world theory, scientific analogy
10.6. Catachresis and satellite metaphors
10.7. Mathematical analogy
11. Thoughts and conclusions
References

Citation preview

Linguistische Arbeiten

407

Herausgegeben von Hans Altmann, Peter Blumenthal, Herbert E. Brekle, Gerhard Heibig, Hans Jürgen Heringer, Heinz Vater und Richard Wiese

Hanna Pulaczewska

Aspects of Metaphor in Physics Examples and Case Studies

Max Niemeyer Verlag Tübingen 1999

Die Deutsche Bibliothek - CIP-Einheitsaufnahme Pulaczewska, Hanna: Aspects of metaphor in physics : examples and case studies / Hanna Pulaczewska. Tübingen : Niemeyer, 1999 (Linguistische Arbeiten ; 407) Zugl.: Regensburg, Univ., Diss., 1997 ISBN 3-484-30407-3

ISSN 0344-6727

© Max Niemeyer Verlag GmbH, Tübingen 1999 Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlages unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Printed in Germany. Gedruckt auf alterungsbeständigem Papier. Druck: Weihert-Druck GmbH, Darmstadt Buchbinder: Nadele Verlags- und Industriebuchbinderei, Nehren

Contents

Acknowledgements Abbreviations 1. Introduction

IX X 1

Part One: The notion of metaphor and its relation to the discourse of physics 2. Approaches to metaphor: past and present 7 2.1. A short history of metaphor 7 2.2. Metaphor, an enemy of science: the early modern view 16 2.3. Metaphor, a friend of science: contemporary physicists on scientific language . . .21 2.4. Current paradigms in research on metaphor in science 27 2.4.1. Linguist's metaphor, philosopher's metaphor 27 2.4.2. Philosopher's metaphor 28 2.4.2.1. True models, objective mathematics? 28 2.4.2.2. Metaphor and physical theory 30 2.4.3. The view of metaphor as the linguistic dimension of a scientific analogy .. .31 2.4.4. Our approach: a preliminary note 32 3. Identifying metaphor in physical science: sorts, functions, and related concepts 32 3.1. Metaphor and related concepts 33 3.1.1. Metaphor and model 34 3.1.1.1. Scientific model: an outline 34 3.1.1.2. Models and metaphors: affinities 35 3.1.1.3. Models and metaphors: distinctions 37 3.1.1.4. Metaphors turned models 41 3.1.1.5. Preliminary specification of conceptual metaphors of functions other than model-theoretical 45 3.1.2. Metaphor and false hypothesis 46 3.1.2.1. Sort crossing and sort-trespassing 47 3.1.2.2. A definition of literal similarity? 52 3.1.2.3. Today's metaphors: yesterday's literal truths? 54 3.2. A working definition of metaphor 56 3.3. Sorts and functions of metaphor in physical discourse 58 3.3.1. Classifications of metaphor in science 58 3.3.2. Sorts 59 3.3.2.1. Extended metaphor 59 3.3.2.2. Linguistic metaphor 60 3.3.2.3. Grammatical metaphor 65 3.3.3. Functions 66 3.3.3.1. Denomination 67 3.3.3.2. Theory and concept formation 67 3.3.3.3. Education 70 3.3.3.4. Style 71

VI

3.3.3.5. Meta-theory 3.3.3.6. Sociology of scientific research

72 72

Part Two: Metaphors in physics 4. Underlying metaphors of everyday thought in meta-theory and the concept formation of physics 75 4.1. Hypostasis 75 4.1.1. Nominalisation as metaphor 75 4.1.1.1. Ontological metaphor 76 4.1.1.2. Grammatical metaphor 77 4.1.1.3. Nominalisation of science and the scientific vision of reality 78 4.1.1.4. A physicist's critique: Bohm's "rheomode" 79 4.1.2. Hypostasis and the emergence of a scientific hypothesis: electric fluid . . . .81 4.1.3. Hypostasis and the constitutive metaphor of optics: travelling light 83 4.2. Spatial metaphor 89 4.2.1. A general outline of spatial metaphor 89 4.2.1.1. The concept 89 4.2.1.2. Container metaphor 89 4.2.1.3. Motion and change 90 4.2.1.4. Orientational metaphor 90 4.2.2. Spatial metaphors in physics: where to find them 92 4.2.3. The metaphor of centrality and the Copernican revolution 92 4.2.3.1. The metaphor of centrality and its perceptual basis 92 4.2.3.2. The central Sun and the metaphor 93 4.2.3.3. The metaphorical aspect of geodynamic hypothesis 98 4.2.4. Spatialisation of time 99 4.2.4.1. Space and time in general language 99 4.2.4.2. Time as movement: the experiential basis 101 4.2.4.3. Time flowing past, or the forward-sliding present? 102 4.2.4.4. "Flow of time" and the absolute theory of time 104 4.2.4.5. The paradox of time flow 106 4.2.4.6. Time as a receptacle of events and the absolute theory of time .. .107 4.2.4.7. Time flow, time receptacle, eternity, and classical determinaton . .109 4.2.4.8. Time as the fourth dimension of space 110 4.2.4.9. An excursion: misconceiving time as space 112 4.2.4.10.The metaphor of space-time curvature 115 4.2.5. Container and orientational metaphors in quantum mechanics 117 4.2.5.1. Visual rendering of energy 117 4.2.5.2. Ranges and states: containers of physical processes 117 4.2.5.3. State as container in quantum mechanics 118 4.2.5.4. Bohr's model of atomic structure 119 4.2.5.5. Energy states of elementary particles 120 4.2.5.6. Band model (theory) of solids 121 4.2.5.7. "More is up" in the energy potential field 129 4.2.5.8. Double/blended recipients of metaphorical denotations: potential wall, potential well, potential barrier 131

VII

4.2.6. Periodic changes 133 4.3. Animism and anthropomorphism 135 4.3.1. Animisms and anthropomorphisms as explanatory and articulatory devices in physical science 135 4.3.2. Spatial representation and self-projection in the interpretative activity of physicists 138 4.3.3. The concept offeree: Newtonian mechanics .141 4.3.4. Anthropomorphism and meta-theory: the secrets of nature and associated concepts 151 4.3.4.1. The secrets of nature 151 4.3.4.2. Terra incognita - science as a voyage; science as a conquest 158 4.3.4.3. Science as venatio 160 5. World theories in meta-theory and the concept formation 162 5.1. The notions "world theory" and "world model" 162 5.2. World machine 163 5.2.1. The clock metaphor 163 5.2.2. The world as a working machine 168 5.2.3. Man and machine in information theory 171 5.3. The world as a text 171 5.3.1. The book metaphor and scientific objectivity 173 5.3.1.1. The independence of the text 173 5.3.1.2. Understanding as non-involvement: the reduction of observing to seeing 174 5.3.2. Alphabet of nature 176 5.3.2.1. Mathematical alphabet and mechanical philosophy 176 5.3.2.2. Alphabet of nature and mathematical notation 178 5.3.3. Bacon's metaphor of two books 178 5.3.3.1. The dignity of natural knowledge 178 5.3.3.2. The "Authorised Version" of the Bible and Bacon's methodological thought 179 6. Stipulative reference extension 181 6.1. Stipulation of meaning: Huygens' notion of sound wave 181 6.2. Invisible light and Roentgen's "invisible rays" 182 7. Assimilative metaphor 184 7.1. "Fluid" electricity 184 7.1.1. The rise and the concepts of the fluid theory 185 7.1.2. Re-definition of substance and the abandonment of the fluid theory 190 7.1.3. Flow of electricity and the electron theory 192 7.1.4. Flow of electricity as educational analogy 192 7.2. The concept of wave 192 7.2.1. The aether waves: mechanical similarity of light and sound 193 7.2.2. The abandonment of the aether theory 195 7.2.3. Further development 197 7.3. Life stories of metaphor: from metaphorical to literal and literal to metaphorical . .197 8. Theory-constitutive and educational metaphors 200 8.1. Constitutive metaphor: waves of probability 200 8.2. Educational metaphor: curvature of space 201

VIII

8.3. From explanation to rhetoric 203 9. Metaphor and style: "figures of speech" in the language of physics 205 9.1. The position of "figures of speech" in the discourse of physics 205 9.2. The arrow of time 207 9.3. Heat death 209 9.4. Maxwell's demon 210 10. Transfer of denotations in the terminology of physics 214 10.1. Metaphors in general language and in the terminology of physics: the general language basis for the transfer of denotations 214 10.2. Types of transfer of denotations 216 10.3. The terminology of physics and related disciplines 217 10.4. Fantasy-metaphor: the case of particle physics 217 10.5. "Mechanical work": underlying metaphor, world theory, scientific analogy . .224 10.6. Catachresis and satellite metaphors 225 10.6.1. Miscellaneous spatial metaphors 226 10.6.2. Similarity in shape or size 236 10.6.2.1. Shape similarity 236 10.6.2.2. Size similarity 246 10.6.3. Animisms and anthropomorphisms 246 10.6.3.1. Donor domain: life and death 247 10.6.3.2. Animation by metaphorical projection of volition 248 10.6.3.3. Donor domain: family relationships 251 10.6.3.4. Donor domain: biological reproduction 252 10.6.3.5. Donor domain: psychophysiological phenomena 253 10.6.3.6. Donor subjects: other physiological states, processes and agencies 254 10.6.3.7. Donor subjects: other biological and ecological notions . . . .256 10.6.3.8. Donor subjects: supernatural beings 257 10.6.3.9. Donor domain: bodily structure 259 10.6.3.10. Donor domain: social values and behaviours 261 10.6.4. Donor domain: sense percepts 263 10.6.4.1. Donor domain: tactile perception 264 10.6.4.2. Donor domain: sensations of hot and cold 265 10.6.4.3. Donor domain: olfactory perception 266 10.6.4.4. Donor domain: auditory perception 266 10.6.4.5. Donor domain: visual perception 268 10.6.5. Hypostasis 272 10.6.6. Donor domain: utensils and instruments, recipient domain: physical instruments, ground of transfer: similarity of function 275 10.6.7. Donor domain: fire 277 10.6.8. Donor domain: fire-arms and shooting 278 10.6.9. Miscellanous donor and recipient subjects 280 10.7. Mathematical analogy 281 11. Thoughts and conclusions 284 References

287

Acknowledgements

My sincere thanks and appreciation go to my academic advisors, who have made this work possible through their encouragement and their criticism. I am deeply grateful to Prof. Dr. Herbert Ernst Brekle and Prof. Dr. Christoph Meinel for their encouragement and their helpful comments at every stage of this research. Regensburg, December 1997

Abbreviations

CERN: European Organization for Nuclear Research. CUP: Cambridge University Press. ISO: International Organization for Standardization. O.E.D.: Oxford English Dictionary. Proc. Roy. Soc.: Proceedings of the Royal Society of London. ScAm: Scientific American.

l. Introduction

A glimpse into the numerous works on metaphor written as recently as the sixties and seventies of our century shows that at that time the overwhelming majority of authors still found it necessary to start their reflections by proclaiming their disagreement with the "classical" view, which regarded metaphor as a means of rhetoric rather than a semantically and cognitively important phenomenon. Today, owing to the numerous works proposing a critical revaluation of the dominant view, it has become rather a truism, at least for linguists and cognitive scientists, to say that the function of metaphor cannot be reduced to the ornamental and literary, that it plays an important role in concept formation, and that the role it plays in language and thought is considerably greater than we used to think. As the view of metaphor as a figure of rhetoric seems already to be obsolete and without adherents, it is nowadays not necessary to treat it as a point of entry in a discussion. The growing interest in metaphor in the last few decades has resulted also in the questioning of the view of science as that field of intellectual activity which, because of its programmatic claim to objectivity, excludes the use of metaphor. Metaphor has also been recognised as an important and indispensable tool of language growth, concept formation and articulation in science, including the natural sciences, with physics being their most rigid representative. Aristotle was the first philosopher to warn against the use of metaphor in the language which we would today call scientific: one should be conscious of the difference between real definitions and mere metaphors. The view of Aristotle, which situates metaphor in the domains of poetics and rhetoric, developed at the beginning of modern science into the idea of a language reform for science, which included the banishment of metaphor from its language. That this program has neither been realised in practice nor is realisable in principle, is the view shared by such authors as Hesse, Harre, Gentner, Hoffman, Boyd, to name only some of the many researchers who point to the applicability of metaphorical processes in the formation of scientific concepts. The interest in metaphor is not confined to the advocates of one particular philosophical orientation, but can be seen as a consequence of a broader stream in the philosophy of science, linguistics, and cognitive science, characterised by the rejection of the so-called objectivist theory of reality and language. The objectivist view assumes that facts are simply given objectively and that they have properties and show relations independent of perceiving subjects, and that acquiring knowledge about the world consists of finding out how things really are in the world. The objectivist mode of thought attributes to the language the role of a reflection of the reality, made up of categories and concepts corresponding to independently existing features of reality; verbal utterances can be judged to be true or false objectively, absolutely, and unconditionally. Common language may also reflect human errors of judgement and perception, illusions and cultural biases, but there is another level of description - science, whose aim it is to find a perfect, objectively true fit between language and reality, and which is able to achieve this goal and is constantly progressing toward it. Finding the language whose terms correspond objectively to facts will enable us to achieve understanding from a universally valid, unbiased point of view, and to communicate about facts in statements which may be objectively judged to be true or false. The objectivist view amounts to the belief in the possibility of a language

which would be, in the formulation of Richard Rorty, an "ultra-thin cushion" between the facts of reality and statement and action, "a language for describing an object which was as little ours, and as much of object's own, as the object's casual powers"1. Sixty years ago, a Polish microbiologist Ludwick Fleck made the proposal, "Erkenntnisinhalt - im großen und ganzen - als freie Kulturschöpfung zu werten"2; "Denn Erkennen ist weder passive Kontemplation noch Erwerb einzig möglicher Einsicht im fertig Gegebenem. Es ist ein tätiges, lebendiges Beziehungseingehen, ein Umformen und Umgeformtwerden, kurz ein Schaffen. Weder dem 'Subjekt' noch dem Objekt' kommt selbständige Realität zu; jede Existenz beruht auf Wechselwirkung und ist relativ."3 The essence of his proposal was to accept the conventionality of knowledge and to "socialise" the theories of science, knowledge, cognition, and truth. In the 60's, assimilated by Kühn in his influential theory of scientific revolution, the socialised concept of the "scientific truth" began to replace the former mainstream view. Currently the essential difference in the cognitive status of science and other kinds of discourse is questioned as much as the notion of an independent fact: facts are theory-laden, and whenever something happens, as many facts are created as there are ways to conceptualise, as many as there are languages to describe the corresponding transaction. Perception and cognition are not separable from each other; the pre-existing knowledge of the perceiving subject structures the contents of perception. It is pointless to speak of the level of "immediately given" or to ask for the level of description defining "what we really are talking about". One of the consequences of this view is the trend against the objectivist mistrust of metaphor, in which metaphor and other kinds of fanciful language can and should be avoided in speaking about facts, as they do not fit reality, and thus cannot contribute to the objective knowledge. Exact sciences take their roots in everyday experience, and the natural source of the concepts they employ are the non-technical notions of everyday experience. Scientific concepts tend to be formed as far as possible in analogy to the concepts of ordinary experience in a process in which the unknown and strange is conceptualised and described in terms of the more familiar. As the decomposition of the continuous flow of experience in ordinary language is partly conventional and to a large extent metaphor-based, the notion of a metaphorfree scientific thought and language is not attainable. Since Kepler, the development of physics has been marked by the growing dominance of the formal language of mathematics, initially augmenting and then increasingly replacing natural language as the means of expression, till it has become what it is today: the fundamental level of description. The formal rigour of the "language" of physics seemed to secure the objectivity of its insights and to preclude any bearing of the metaphorical on its discourse. As a "language", however, the mathematical formalism alone is incomplete: it lacks reference. Mathematical formulas must be somehow attached to measurable things in the world; language and non-mathematical conceptual structures are needed to provide the correspondence. Physics becomes vulnerable to metaphor - it is our goal to clarify in which ways.

1 2 J

Rorty 1985: 2. Fleck 1983: 46. Ibid.: 48. Italics in original.

There is no simple definition of metaphor to start from. The "classical" view, based on that of Aristotle, was subjected to a damning criticism in the last few decades by authors such as Black, Richards, Johnson, to name but a few. Today, we are confronted with a proliferation of the theories of metaphor and of the literature on that subject, making a clear delineation of what "metaphor" is increasingly difficult. A bibliography of metaphor edited by van Nopen in 1985 comprises some 2200 titles; a supplement, or the second volume, edited five years later, nearly as many. Fifteen years ago, Booth4 remarked anecdotally that if the number of studies on that subject were to increase further at the same rate, by the year 2039 there would be more students of metaphor than there will be people on the earth. As a preliminary step in the analysis of the notion of metaphor as it is currently understood, it is necessary to point to the complexity of the current discourse on that subject. Metaphor is a subject of analysis in several fields of study: literary criticism, linguistics, history and philosophy of science, anthropology, sociology and the study of religion. Each of these focuses on different aspects and kinds of metaphor according to its particular interests. The study of literature, whose interest in metaphor is, for historical reasons, the longest and most widely acknowledged, focuses on novel, imaginative metaphors in poetry and artistic prose, its emotive quality and the contribution to the stylistic aspects and aesthetic impact, in particular authors and literary works, the metaphorical stock of particular literary epochs and literary movements. The history and the philosophy of science deal with the problems of applicability of the notion of metaphor to exact sciences and examine its affinities with scientific models and analogies. The kind of metaphor they are interested in is rather different from the literary one. Metaphors of that kind are not individual and subjective but shared by a scientific community; stable and consistent as opposed to the "temporary", passing literary metaphors; more explicitly cognitive rather than figurative or emotive; often natural, unforced, and "imperceptible"; capable of functioning consistently and intersubjectively as an instrument of thought; leading sometimes to new predictions; and entering relationships with a mathematicalised scientific discourse. In the study of science, the notion of "metaphor" overlaps with the notions of model and analogy, and sometimes it is used in a rather inflated way to refer to other kinds of imaginative thinking, concept formation, and speculative hypothesis.5 Cognitive science analyses the contribution of metaphor to concept formation, the growth of knowledge and the ability of problem solving, mostly in connection with the notions of imagery and analogy. Linguistics deals with questions of meaning constitution and meaning change, examines the role of metaphor in the everyday speech, and charts the process of the "death" of metaphor and its role in language growth. Sociology, anthropology, and the study of religion self-reflectively trace the metaphorical origin of some of the notions they apply. As a result of this prolific application of the notion of metaphor in various fields, the notion itself has undergone considerable semantic stretching. It requires some "leap of imagination" to understand what makes it possible to speak of the expression "the roses in Booth 1979: 47. Cf., for example, Jones 1982; MacCormac 1976.

her cheeks", the mechanist world view, and social Darwinism as manifestations of one and the same process. In spite of their different foci of attention, all the disciplines taking interest in the metaphorical process share much of the theoretical background. In the bibliographies attached to works on metaphor, the works of I. A. Richards, Black, Hesse, Ricoeur, Levin, Turbayne, and Johnson are typically included. We selected some of these for the presentation of a short history of the development of the notion of metaphor at the outset of our work. We have chosen the historical outline as one of the possible ways to expose with some systematicity a variety of issues associated with the question of defining metaphor for the purpose of its identification where it contributes to the physical discourse. The contemporary views on metaphor mentioned are those which expose the cognitive dimension of metaphor and those which stress the ubiquity of metaphor in concept formation and language growth. In view of the existence of a rather extensive and, to some extent, self-repetitive body of theoretical reflection on metaphor, which is embedded in the discussion of model and analogy in exact sciences, we think that the discourse on this subject needs a further impulse in the form of a broad specification of metaphors in physics rather than a further generalisation on the basis of scarce sample data. The main body of our work consists of the analysis of a collection of metaphors, which together illustrate the view of metaphor as an indispensable and ubiquitous means of thought and articulation in physical science. It is preceded by some preliminary generalisation which had to be undertaken in order to select our examples (to determine what counts as a metaphor in physics), and to systematise what would otherwise be a random collection of heterogeneous data. The place for the linguistic analysis of metaphor in science might, at first glance, seem limited to examining the extension of the terminology through transfer of denotations leading to polysemy of lexical items (catachresis) because the semantics of physical terms is equivalent to the physical theory itself. There is no need to reconstruct the semantic field of a physical concept through analysing its use as is the case with the concepts of everyday language because in scientific terminology meanings are.precisely defined in their interrelations with other concepts and fixed by formal definitions and mathematical formulae, so that a change in their semantics is a change within the physical theory itself. Thus, it seems that the study of semantics and semantic change in physical science is equivalent to the study of the structure of the physical theory and its history, and belongs to the domain of the philosophy and history of science. Is there, then, besides catachresis, any further room for the linguistic analysis of scientific metaphor? In this study, we shall identify and illustrate diverse types of metaphor functioning within the discourse of physical science on diverse levels - from terminology to the underlying metaphysical assumptions guiding the scientific enterprise and determining the kind of questions asked. The novel, transient metaphors of a literary kind, will be of no interest to us; we will deal with metaphor as the means of the formation of lexicalised denotations, meanings and intersubjectively shared concepts. This kind of metaphor, conventionalised by repeated application, is to be found in everyday language and thought as well as in science, and part of our approach to the subject of scientific metaphor will be tracing the relationships between the metaphorical stock of everyday language and the formation of scientific concepts. Thereby we will provide support for the thesis of the ubiquity of metaphor in science from a linguistic perspective not included in the science historian's view of the subject.

Our point of cognitive access to metaphorical processes in natural science is to accept that metaphor is a heterogenous phenomenon whose parts are out of phase with each other, approachable from many standpoints, none of which comprises the phenomenon in its entirety. Neither does it come in neatly classified compartments; it is a multiflow of items allowing certain accentuations which we try to pin down. Whatever is said of metaphor other than the most general minimal definition applies only to some of its aspects and excludes others. This is unavoidable because to analyse metaphor is to analyse the nature of creativity, which by definition resists attempts for an exhaustive account and cannot be fully pushed into the framework of any one-sided approach. Because in this work we want to conduct a multilevel analysis of metaphor embracing many aspects both interconnected and partially out of phase with each other, we will try to make the best possible use of eclecticism, taking our samples and ideas from wherever we find them. We find this eclectic approach adequate to the heterogeneous nature of the phenomenon itself. We systematise our analysis by differentiating at the outset the various levels on which metaphors function in the physical discourse. We assume that the concept of metaphor can consistently be applied to a whole range of linguistic and conceptual phenomena, including those based on an easily-grasped recognition of similarity between two conceptually structured domains of experience and those where this similarity is a "projection" from a known domain to a less-known one made into an object of reflection. We accept the notion of metaphor as applying to a whole spectrum, ranging from a projective transfer of structure, through an extension of a word's reference on the basis of clearly recognisable criteria, to the transfer of denotations leading to polysemy of lexical items. The domain of new experience for which we apply metaphor as a means of communicating or as conceptual manipulation can be as narrow as a newlyinvented instrument and as broad as the notions of nature and the world. We will find one end of the spectrum of the metaphoric process in the terminology of particular branches of physics, the other where historical epochs seek to formulate their attitudes towards the object of natural science as a whole.

Part One: The Notion of Metaphor and its Relation to the Discourse of Physics

2. Approaches to metaphor: past and present The first section sketches briefly the approach which has been handed down to us by the previous generations, plus the beginnings of the change of attitude in our time, and presents in some length the views of those researchers who focus upon the way in which metaphor underlies our thought and language, leading to the growth of concepts and the change in word meanings. Our survey excludes the period of the beginnings of modern science in the 17th and early 18th century. It was this era that first saw the formation of the views on the relationship between metaphor and the language of science, which was characterised mainly by the sharp criticism of metaphorical language as being inappropriate to the aims of scientific research. The philosophers' approach to metaphor and the language of science in general which was characteristic of that time will be dealt with in the second section. These views contrast sharply with the contemporary physicists' recognition of the limitations and creative aspects of language as the instrument of expression in their field of study; the latter form the subject of the third section. The last section characterises briefly the mainstream tendencies in the contemporary studies on metaphor in natural science. By means of this presentation, we hope to achieve a comprehensive account of what has happened to the views of language on one hand, and to the views of the physical research on the other, to make possible today's meeting of "physics" and "metaphor" in one phrase.

2.1. A short history of metaphor The earliest Greek philosopher who may be regarded as having initiated the traditional suspicion of metaphor is Plato. In "The Republic", X, Plato speaks in favour of banishing philosophically uneducated imitative poets from philosophy: the power of poetry and myth can influence conviction and is open to the potential of being misused. His attack is directed against the poets and the sophists who misuse language leading others away from truth, and has often been interpreted as an attack against figurative language in general. An extended treatment of metaphor is to be found in Aristotle. For him, metaphor is a powerful means of gaining insight and making a persuasive argument. Aristotle places this treatment of metaphor in Poetics, and thus puts the basis for the traditional perspective of situating it in the literary context. He defines metaphor as giving a thing a name that belongs to something else; the transference being either from genus to species, or from species to genus, or from species to species, or on grounds of analogy.1 In "Rhetoric" (1405a), Aristotle claims that it may also be of great value in prose, but only as long as it is fittingly applied: '

Aristotle: Poetics, 1457b.

... metaphors, like epithets, must be fitting, which means they must fairly correspond to the thing signified; failing this, their inappropriateness will be conspicuous.

He discusses at length the difference between appropriate and inappropriate metaphors, and the basis of his judgement in this issue is the appropriateness of the relevant similarities in which various metaphors are grounded. Although Aristotle praises metaphor as the means which can render poetic diction and prose clear and interesting, his treatment of it includes several notions which contemporary researchers have felt obliged to attack: • the metaphorical transfer is located at the level of individual words; • metaphor is seen as a deviance from literal usage, because it gives a thing a name which does not properly belong to it; • the command of metaphor is a matter of genius, available only to some talented individuals; • metaphor is based on objectively pre-existing similarities between things. All of these views survived well into our century, only to be seriously questioned in the 60's. Two centuries after Aristotle, Cicero (De Oratore, 3.39) sees metaphor as a brief similitude contracted into a single word; later, Quintilian (Institutio Oratoria, VIII, VI. 8-9) describes it as a shorter form of a simile, in which the object is actually substituted for the thing. Like Aristotle, although praising metaphor, at the same time they warn against its improper use as when the dissimilarities surpass resemblances, or when it is overused. They do not attribute to it any cognitive function beyond being an implicit comparison. In medieval rhetoric, the judgement of metaphor is not unanimous. There are warnings against metaphors as the means by which the attention is diverted from the real qualities of the object being described. More positive evaluations refer to the language of the Holy Scriptures. St. Thomas Aquinas regards metaphor as inevitable in speaking about God as certain spiritual truths are not directly accessible - God cannot be known or described directly. In the times when modern science is beginning to develop, it is mistrust that clearly wins the field; metaphorical language is judged as not adequate for the aims of scientific communication. We expound the early modern philosophers' attitude to language in general and metaphor in particular in more detail in the next section of this chapter. At the end of the eighteenth century, Kant (1790) offers a fresh insight into genius and imagination, including a positive reference to symbol (which in this century became a source of inspiration for Langer, and for Blumenberg in his theory of absolute metaphor). For Kant, our symbolic skill expresses the general human capacity for creative thinking. He speaks of Übertragung der Reflexion über einen Gegenstand der Anschauung auf einen ganz anderen Begriff, dem vielleicht nie eine direkte Anschauung direkt korrespondieren kann.2

He reflects on the mechanist metaphor in its application to the state, maintaining that imaginative metaphoric representations result in our ability to manipulate concepts which could not be achieved through literal representation: ... zwischen einem despotischen Staate und einer Handmülle ... zwar keine Ähnlichkeit [besteht], wohl aber zwischen der Regel, über beide und ihre Kausalität zu reflektieren.3

2 3

Kant 1790, 1960: 11. ibid.

The Romantic poets paid due tribute to metaphor as the means of intuitive insight and to the creative imagination in general. However, they mistrusted science and explored art and religion as the tracts of experience beyond and above the limits of mere reason. Thus their appraisal of metaphor was accompanied by the claim of there being a wide gap between sterile scientific understanding and artistic insight, which contributed considerably to the confinement of metaphor to a ghetto of special, poetical use. Nietzsche continues the tradition of Romanticism's affirmation of metaphor, and refuses to see metaphor as any different from the proper use of words. He sees metaphorical understanding as the omnipresent principle of thought and language. For him, metaphor is not a matter of substituting words but the base of both perception and its rendition through language. He articulated what Bühler, Wittgenstein and others were to repeat in this century - that the same words are used to name innumerable different, albeit similar, experiences; this is his reason for claiming that we experience reality metaphorically. He was conscious of the process of conventionalisation of metaphorical understanding to the point at which it appears as literal.4 However, his treatment of metaphorical process as the basis of thought seems to have been disregarded by philosophy and identified with the general attitude of the Romantic poets, favourable to metaphor, but critical of scientific understanding, and thus preventing the reflection on the association between them. The period of the dominance of logical positivism was also, for obvious reasons, unfavourable to metaphor. The belief that scientific knowledge could be reduced to a system of literal sentences, whose truth could be separately verified, let metaphor be regarded as philosophically ignoble; its meaning, that is, its truth claims, could be captured by a literal paraphrase. Logical positivism had been dismissed by the mid-twentieth century, and the claim of literal paraphrasability of metaphoric statements has also been subjected to criticism and finds little support. Wegener was among the earliest linguists to pay attention to metaphor as the means of language growth. He regarded meanings as contextually determined and metaphor as the means of word meanings "fading in predicational use" ("Ablassen im prädikativen Gebrauche")5 caused by habituation of use in a novel context. So zeigt sich uns eine Entwicklungsreihe des metaphorischen Gebrauchs, welche damit anhebt, dass zum Verständnis des metaphorischen Prädicats ein Hinweis in der Exposition erfordert wird, das Subject unter diesem Bilde zu denken, und die damit schliesst, dass man das Bild, durch welches der metaphorische Ausdruck herbeigeführt wird, gar nicht mehr empfindet.' This line of thought was continued in the beginning of our century by Mauthner (1912: 451), who claimed: Unsere Sprache wächst durch Metaphern. Und zwar kann man sagen, daß jede Metapher zuerst bewußt gebraucht wird und in den Organismus der Sprache, als Zuwachs, erst dann eingetreten ist, wenn man sie nicht mehr als Metapher fühlt. Mauthner speaks of metaphor and analogy as "treibende Kräfte der Sprachbildung", and of "Alleinherrschaft der Metapher im Bedeutungswandel". In his view, Für den Weg, auf welche ein bestimmtes Wort neue Bedeutungen erobert, für jeden einzelnen Schritt des Bedeutungswandels der Sprache ist die Bezeichnung Metapher die beste; wer sich erst Cf. Nietzsche 1873, quoted in Böning 1988: 111, 170, 177, 183. Wegener 1885, 1991:54. ibid.: 51.

10 diese Anschauung von der eigentlichen Sprachgeschichte ganz zu eigen gemacht hat, der kann nicht daran zweifeln, daß jeder Schritt in der Geschichte des Bedeutungswandels dieselbe geistige Tätigkeit war, die in der Poetik als eine Metapher erklärt wird ... Es gehört aber zum Wesen der Sprache, daß die geistreichere Beobachtung, die nur bei der ersten Anwendung der Metapher notwendig war, aus dem Bewußtsein schwindet, daß das Wort allmählich unbewußt an seinen erweiterten Sinn erinnert.7 Die zwei oder die hundert "Bedeutungen" eines Wortes oder Begriffes sind ebenso viele Metaphern oder Bilder, und da wir heute durchaus von keinem Worte eine Urbedeutung kennen, da die erste Etymologie unendliche Jahre hinter unsere Kenntnis von ihr zurückliegt, so hat kein Wort jemals andere als metaphorische Bedeutung.8

Metaphor depends on comparison of two things necessary for each act of concept formation in general ("der elementare Zwang des Vergleichens bei der Begriffsbildung"*). There is, however, a difference between naming an object and applying a metaphor: Nahe Ähnlichkeiten konnten sofort durch Begriffe oder Worte festgehalten werden. Der Bedeutungswandel besteht ... in der metaphorischen ... Ausdehnung des Begriffs auf entfernte Ähnlichkeiten.10 At the same time, Mauthner (1913: 240) seems not to be attributing an absolute, objective character to these similarities, that is, abstracting them from the perceiving subject: Aus dem Wortgebilde des Einzelnen ergibt sich die Möglichkeit, Ähnlichkeiten zu sehen und die Vergleichung kurz und schlagend durch eine Metapher auszudrücken. Der Hörer kann die Metapher des Redenden nur verstehen, wenn er eine gleiche geistige Situation, ein gleiches Weltbild ihn befähigt, die angeregte Vergleichung ebenfalls vorzunehmen. With respect to the function of metaphor in the growth of language, Mauthner differentiates between "Namengebung" and "Begriffserweiterung", or "metaphorische Neubildung" and "metaphorische Erweiterung". (In what follows we similarly talk of metaphor as including both aspects, which we designate as stipulative catachresis or transfer of denotations, and extension of reference.) Mauthner recognises also that the same process of meaning change through metaphorical extension takes place in the scientific concept formation, and vigorously opposes the view that exact sciences such as chemistry and physics are distinguished by a language that is qualitatively different from the vague and fuzzy everyday language. In the Anglo-Saxon world, an early attempt to further the significance of metaphor in common language is found in Langer (1949). Inspired by Wegener's ideas, she perceived the ubiquity of metaphor and the process of literalisation of metaphorical meaning: In a genuine metaphor, an image of the literal meaning is our symbol for the figurative meaning, the thing has no name of its own... But if a metaphor is used very often, we learn to accept the word in its metaphorical context as though it had a literal meaning there.. .The great extent and frequency of its metaphorical services have made us aware of the basic aware of the basic concept in virtue of which it can function as a symbol in so many contexts; constant figurative use has generalised its

Mauthner 1906: 120-131. Mauthner 1912: 451. ibid.: 467. ibid.: 488. Langer 1949: 113-114.

11 [...] The use of metaphor ... is the power whereby language, even with a small vocabulary, manages to embrace a multimillion things; whereby new words are bom and merely analogical meanings become stereotyped into literal definitions ...""

Langer's theory is closely bound with the evolution of speech, in particular with its function of giving something a name. Literal language for her is the "repository of language". She argues persuasively in favour of broadening the concepts of meaning and metaphor to include metaphor as new meaning. Brown (1958), too, identifies metaphor as one of the two basic forms of semantic change. All these writers recognised what today has become a matter of course: metaphor functions in the lexicon as a process of generalising meaning change; new literary language is made by the emergence and then the dying or fading of a metaphor. The contemporary history of metaphor as a primarily cognitive phenomenon is frequently said to have originated with Richards' "interaction view" of metaphor which he initiated and which gained currency after it was developed and popularised by Max Black some thirty years later. Richards (1936, 1979: 94) questioned the frequently implied assumption that metaphor is a matter of language alone, and is situated at the level of individual words. Instead, for him it is a ubiquitous vehicle of thought: The traditional theory noticed only a few of the modes of metaphor; and limited its application to the term metaphor to a few of them only. And thereby it made metaphor seem to be a verbal matter, a shifting and displacement of words, whereas fundamentally it is a borrowing between and intercourse of thoughts ... Thought is metaphoric, and proceeds by comparison, and the metaphors of language derive therefrom.

Richards introduced into the analysis of metaphor the descriptive terms vehicle, tenor and ground; today, they have already lost some of their popularity - many authors prefer to speak of explanandum and explanans, or primary (principal, recipient) and secondary (subsidiary, donor) subject. The "interactive view" of Black, inspired by Richards' early work, is probably the most widely acknowledged contemporary approach to metaphor, and its introduction in the early 60's marks the beginning of the rapid growth of philosophical interest in metaphor. Among others, it has been adopted by Mary Hesse in her influential works in philosophy of science in which she develops the idea of science being essentially metaphoric, and the concept of scientific explanation as consisting, at least to some extent, of a metaphorical redescription of the domain of explanandum. For Black, a metaphor is neither merely the means of economic, compact language use translatable without loss of cognitive content into a literal paraphrase (as in "substitution view"), nor an implicit comparison expressing that "X is similar to Υ in respects A, B, C" (as in "similarity view"). Some trivial cases of metaphor are adequately described by the "substitution" and "comparison" views, but only those instantiating "interaction" are of importance in philosophy. The main assumptions of the "interactive view" are: A metaphorical statement has two subjects - a 'principal' subject and a 'subsidiary' one. These subjects are best regarded as 'systems of things', rather than 'things'. The utterance works by projecting upon the primary subject a set of'associated implications' characteristic of the subsidiary subject. These implications usually consist of 'commonplaces' about the subsidiary subject... The

ibid.; 115.

12

maker of a metaphorical statement selects, emphasises, suppresses, and organises features of the principal subject by implying statements about it that normally apply to the subsidiary subject.13 "Associated implications" or "commonplaces" are the man-in-the-street's knowledge of the metaphor's subjects, a layman's knowledge of men and wolves. Black argues14 that not only is the "primary subject" influenced in the process, but our view of the secondary subject also undergoes changes. In Hesse's (1966: 163) wording, ... its associations come to be affected by assimilation to the primary; the two systems are seen as more like each other; they seem to interact and adapt to one another ... Since Black's original publication in 1962, an explosion of literature on metaphor has taken place. Numerous writers have analysed metaphor as a process of concept formation and questioned the traditional way of seeing the distinction between metaphorical and literal meaning. The advocates of the new perspective are more or less directly indebted to works of Wittgenstein and his notion of "family resemblance" (developed later by Rosch and her coworkers in their influential prototype theory of categorisation). For Wittgenstein, there is no need of a set of necessary and sufficient properties shared by all the instances of a term. We may recognise instances of a term through some of their features being shared with some other instances of the concept in question (the various members of a given class are connected by "family resemblance"). This notion suggests the possibility of the change of a concept through recognising as its instances things which are at variance with the hitherto known instances. Wittgenstein's concept leaves little room for differentiation of the denotation and "the set of associated commonplaces" of a concept. Each act of classification of a new as an instance of the old may constitute a shift of the meaning of the old concept through the new subject's properties entering the network of family resemblance. In Schön's (1963: 28) formulation, In the ordinary application of concepts to things, the concepts leave the process as they came in. Everything that is not old in the thing (not assumable under the concept) is put aside. Not every application, however, leaves the concept unchanged; if a concept is used to classify an object differing considerably from the hitherto-known instances, its meaning may itself become affected. Wittgenstein dynamised the concept-instance relation, pointing out the inadequacy of the notion of the stability of concepts as sets of fixed "sufficient and necessary" properties. His merit lies in recognising the creative character of each act of classification: all language occurs in novel contexts, each predication includes application of a set of more or less abstract constraints to a novel instance. In this way he diminishes the difference between the application of a concept, the change of a concept, and the formation of a new concept. Implicitly, also the difference between the literal and metaphorical as acts of typical versus novel categorisation becomes abated. Acknowledging Wittgenstein as her source of inspiration, Hesse (1988: 3) says: The shifts of meaning undergone by predicates applied in FR (family resemblance) classes are also like metaphoric shifts of meaning, for they depend on similarities and differences in some respects and in given contexts between the objects to which a given FR predicate is applied, and this is at least part of the way in which metaphors work. The extensions of meaning that occur by means of Black 1962: 44. In the initial formulation of his view, later moderated.

13 similarities and differences in metaphor are only more striking examples of something that is going on all the time in the changing and holistic network that constitutes language. In this sense metaphorical meaning is normal, not pathological, and some of the mechanism of metaphor is essential to the meaning of any descriptive language at all ... The literal/metaphoric distinction is properly a pragmatic, not a semantic use. Literal use is most frequent use in the familiar contexts - that use that least disturbs the network of meaning ... but it does not imply that the semantic bases of the two sorts of expression are radically different.

That is why in analysing metaphor we should not care so much about where to draw the line between the metaphorical and the literal, but, rather, see our objective in investigating the phenomena of metaphorical extension and change of meaning, and the like.15 Bosch (1985) shares Hesse's view that it is not necessary to postulate additional mechanisms for the production and comprehension of metaphorical speech beyond those which are applied in the processing of "ordinary", literal language. A certain amount of vagueness and ambiguity is necessary for the vocabulary of any language because language must generalise - it cannot contain special expressions for each particular state of affairs. In order to speak of a thing, we have to assign it to a linguistically and conceptually available category on the basis of more or less exact correspondence between the thing and the category. In Bosch's semantic theory, the meaning associated with a word has the form of a "stereotype" - a concept closely akin to the notion of "synchytische Begriffsbildung", worked out half a century earlier by Karl Bühler, a forerunner of modern dynamic (contextdriven) semantics (cf. Brekle 1983). The meaning of a word (its "stereotype") consists of typical properties of its referents and, like Rosch's "natural categories", has a radial structure with some properties being more central to it, others playing a more marginal role. For Bosch, as for Bühler, each component of word meaning may be invalidated (or "abgedeckt") by the circumstances of its use. He describes the difference between the metaphorical and the literary application of a word as lying in the fact that in a metaphorical expression it is a relatively constant, central component of a word's meaning, or "stereotype", which becomes invalidated by the situational or textual context, whereas the literal usage preserves the central components of meaning (stereotype). The obliteration of one or more central properties of a word through a metaphor aims at naming a cluster of properties which together belong to the "stereotype" of a word, but for which there is no "own" formulation in the language given. As there is no difference between the semantic component and the encyclopaedic or "commonplace" knowledge, the difference between metaphor and literal speech is merely gradual. Its measure is the centrality of the properties which are left out of the activated part of a word's meaning in an actual utterance. Cohen and Margalit (1972) and Abraham (1975) also give metaphor a definition similar to Bosch's, in terms of the exclusion of some specified part of the usual meaning. For Abraham (1975: 8), metaphor is to be approached by means of the notion of topicalisation of components in decomposition of lexical meaning; a metaphor upsets the semantic structure of the donor and the recipient subjects ... shifting the feature of thematic dominance from the head of ... a semantic concept to one of the satellite (determining) features." The claim articulated already in Hesse 1971. Abraham 1975: 23.

14 Cohen and Margalit (1972: 735) also define metaphor in terms of component!al analysis of meaning: The metaphorical meanings of a word or phrase in a natural language are all contained ... within its literal meaning or meanings. They are reached by removing any restrictions in relation to certain variables from the appropriate section or sections of its semantic hypothesis ... Note that in all such cases the variable or variables that have their restrictions removed may be expected to be fairly near the beginning of the ordered sequence of relevant variables. Any such variable must be a fairly important one. Otherwise there would not be sufficient distance between the restricted meaning and the derestricted one for the latter to be regarded as a metaphor.

Our reservation concerning the linguistic approach to metaphor in terms of decomposition of meaning into selectional restrictions or components of a stereotype is that it frequently implicitly reduces metaphor to the level of words and sees it as based always on the recognition of a pre-existent similarity of two subjects, the meaning of one including some component features recognised as characteristic of the second. Such a mechanism is quite applicable in explaining the reference extension of some words and transfer of denotations, including scientific termini. However, any similarity-based approach to metaphor does not account satisfactorily for numerous verbal expressions of extended conceptual metaphors. It cannot adequately explain those cases of metaphoric structure transfer which make it problematic to speak of a pre-given "cluster of properties" to be expressed, as the similarity between the thing to be named and the old concept results from rather than gives an objective justification to the metaphoric process. With reference to this latter type of metaphor it seems more appropriate to speak of imaginative projection from one domain to the other. The judgement of similarity makes sense only "from within" the metaphor, that is, within the framework emerging out of the metaphorical displacement, giving the same structure to the two domains of experience. A thesis of Black's (1962: 37) was that it ... would be illuminating in some of these cases to say that the metaphor creates similarity than to say it formulates some similarity antecedently existing.

Thus, metaphors create perspectives to see the world from: they are indispensable for seeing connections which are not there until once perceived, but present afterward. They help to see aspects of reality which they themselves help create. The formulation of the similarity is a creative process whose result is not strictly determined by the semantics of words. In the meantime, this severely criticised (cf. Khatchadourian 1968) suggestion, which seemed to some researchers to amount to the claim that metaphor creates similarities "out of nothing", has found independent support. Among the writers who pointed out the existence of this aspect of metaphorical transfer, Schön (1963), inspired by Wittgenstein's ideas, was among the earliest. For Schön, metaphor is another name for the displacement of concepts, which is one of the ways in which new concepts are formed. The new concepts emerge out of old ones through a process of their novel application. He rejects the popular view that the metaphorical displacement of a concept is based on similarity between the familiar type of situation and the novel one because such a similarity is a post-factum effect of the displacement: the notions consisting of the shared properties of the old and the new come as the result of the process; we do not have them to begin with. Instead of postulating "comparison" between the old and the new as the basis of metaphor, he prefers to speak of a juxtaposition through which we are able to find

15

in the new situation aspects related in the manner of the old which we had not previously seen in the old. Schön, like Black, stresses the two-way character of the metaphorical process. The carrying over of the old concept to a new situation does not proceed with a perfect freedom, as the new situation already has some sort of structure and resists some transposition and interpretation; what results is a mutual adaptation leading to adjustment, in which the old theory and the new concept-structured situation are modified in various ways to suit each other: "With the development of the concept of cold war, our notion of war has changed as well as our notion of the international situation." " Schön's (1963: 60) analysis makes clear that metaphors are not to be located on the level of particular verbal expressions, like words or phrases: ... from a symbolic relation, once established, an indefinite number of possible related aspects of the new situation can be generated and considered. Metaphors are easily carried and can be made to generate indefinite series of expectations which need not be remembered since they can be generated again. They have the condensation essential to instruments of thought.

Similarly, Blumenberg (1960: 16-17) recognizes the primacy of the conceptual (as opposed to verbal) aspect in certain kinds of metaphors saying that Metaphern in ihrer hier besprochenen Funktion gar nicht in der sprachlichen Ausdruckssphäre in Erscheinung zu treten brauchen; aber ein Zusammenhang von Aussagen schließt sich plötzlich zu einer Sinneinheit zusammen, wenn man hypothetisch die metaphorische Leitvorstellung erschließen kann, an der diese Aussagen 'abgelesen' sein können.

In this view, "metaphor" is situated on the level of concepts; it can be relatively directly verbalised but not necessarily so; in the latter case it is only indirectly "deducible", that is, it can be reconstructed on the basis of a complex of linguistic formulations. Lakoff and Johnson (1980: 153) take as the point of entry for their study the assumption that "the metaphor is primarily the matter of thought and action and only derivatively a matter of language", meant to express much more than the trivial truth that the conceptualisation must precede the verbal articulation, or that nothing can be verbally expressed before it has been conceived of. Their interest focuses upon the existence of a vast class of metaphorical expressions which are derived from underlying, covert metaphors, whose existence usually escapes the attention of the speaker. A great part of everyday speech is based on such covert metaphors whose function is to provide us with the possibility of conceptual and linguistic handling of one kind of phenomena through imposing upon it a structure borrowed from another, better defined kind of phenomena. Such underlying metaphorical structures are invisible for the speaker who utilises them because they are stabilised parts of our conceptual equipment. Think of our self-evidently relevant way of talking about arguments: winning and losing, attacking weak points in the opponent's argument, making indefensible claims. All that illustrates that the underlying structure of the argument concept is one characteristic of the concept of war. Many of us (linguists included) would tend to oppose the idea that using the same vocabulary to describe facts concerning wars and arguments is metaphorical speech, arguing that, rather than a structure transfer being involved, war and argument have inherently the same structure, that is, that the words "attack", "defend", or "position" have more general meaning, allowing them to be applied to both fields. This is the type of view that has been 17

Schön 1963: 55.

16 critically accounted for by Schön (1963) as a process of thinking the metaphorical process backwards, mistaking the final for the initial stage, in which the product of a metaphor - the result of the interaction of two subjects - is mistaken for the very meaning of the concept in question, pre-given in this form to be applied to both domains. This skeletonising of a concept in order to see what is common to the various applications of a term, or concept, is a post-factum undertaking, and in fact the common core often cannot be grasped itself without the use of the very same metaphor (think for example of the common core of physical and psychical strength: the ability to resist outside forces, and the like). In the metaphors analysed by Lakoff and Johnson, there is often no available non-metaphorical description of the primary subject,18 rendering the claim about any pre-existing similarities hardly defensible. An important aspect of Lakoff and Johnson's analysis is the articulation of the idea that numerous metaphoric expressions are verbal tokens of the ways in which the imagination links cognitive and bodily structures. Most basic metaphors are those which project our bodily experience upon other domains - as when we speak of entering a relationship (utilising the metaphor "relationships are containers") or breaking ties (psychical linkage as a metaphor where the secondary, or donor, domain is the physical linkage of two objects). These arguments against the view of metaphors as being implicit comparisons, based on similarities inherent to the two subjects prior to their metaphorical exposure, are relevant to the issue of metaphor in a scientific inquiry: sciences like physics tend to include assertions about those features of the world that are beyond all possible experience, and that must be formulated in a language stemming from the actual experience. Comparisons, however, are essentially possible only for realms known from experience. It is an imaginative projection from the known to the new rather than a comparison which is involved in hypothesising e.g. about the processes taking place on the subatomic level. It is through metaphorical processes that we are able to reason and speak about unobservable events and entities - through projecting upon them a structure of observable ones. That the function of metaphor is to help shape largely unknown, unstructured content domains has been generally recognised by linguists and cognitive scientists within the last two decades, also with respect to scientific thought; e.g., Kittay (1987: 226-227) argues that When the new sciences of electricity, magnetism, genetics, and molecular biology emerged, they were exploring previously unarticulated content domains ... It is precisely to provide such an articulation that we often require metaphor - in the case of metaphor, the structure of another, articulated or formed content domain is used to provide the articulation of the as yet unarticulated or unformed content domain.

2.2. Metaphor, an enemy of science: the early modem view In the period when modern science began, the linguistic problem was seen as very important in the consideration of the scientific method. The approach to language of those involved in the pursuit of the natural phenomena was characterised by a sense of inadequacies and

Such metaphors, for which there is no literal equivalent, are sometimes termed "suppletive" and contrasted with "supplementary" metaphors of rhetoric, the terms introduced by Anderson 1992: 71.

17 dangers inherent in all ancient and modern languages; "redundancy, anomaly, ambiguity and equivocation".19 Many of the leading figures in the scientific revolution, such as Bacon, Hobbes, and Boyle, urged the necessity for a reform of language to make it fit for science, and the Royal Society actually formed a committee for improving the English tongue, "particularly for philosophical [i.e. scientific] purposes";20 the society's members were urged to strive for the ideal of "bringing all things as near the Mathematical plainnesse as they can".21 Jones (1932: 319) claims that the distrust of language at that time was carried to such extremes that "all verbal media of communication were considered one of the greatest obstacles to the advancement of learning". Linguistic defects discovered in natural languages were multiple, they included the irregularity of the grammatical rules, ambiguity of words and the existence of synonyms; among them, metaphor, conveying the connotations from the ordinary use of a word employed in a scientific treaty, was an important point. Bacon (1620, 1960,1: 56) overtly expresses this antipathy to language. He believes that since words were invented to satisfy inferior intellect, they either stand for things which do not exist at all, or inaccurately represent the truths of nature: ... For men believe that their reason governs words; but it is also true that words react on the understanding; and this is that has rendered philosophy and the science sophistical and inactive. Now words, being commonly framed and applied according to the capacity of the vulgar, follow those lines of division which are most obvious to the vulgar understanding. And whenever an understanding of greater acuteness or a more diligent observation would alter those lines to suit the true division of nature, words stand in the way and resist the change.

It is axiomatic with Bacon and his era that there are true divisions of nature to apply words accurately to. Among the linguistic defects which became subject to criticism were a word's possessing many meanings, and the use of metaphors. From the Aristotelian view of metaphor as the transference of a name from its proper object to some other object, it was natural to fear that a transfer of meaning essential for a metaphor was likely to deceive those who had taken the word or name in question as signifying only the original object. If a word was to be a match for a thing or action, metaphor was undesirable and should be banned from scientific language. Berkeley (1721, 1969: 203) demanded that "philosophers should abstain from metaphor", and Locke (1706) addressed the question of "the proper use of words" saying that The use, then, of words is to be sensible marks of ideas, and the ideas they stand for are their proper and immediate signification ... It is true, common use by tacit consent appropriates certain sounds to certain ideas in all languages, which so far limits the signification ofthat sound, that unless a man applies it to the same idea, he does not speak properly ..."

Locke criticises "Inconsistency" in using words as "a great abuse of Words", and Obscurity, by either applying old Words to new and unusual Significations ... Words being invented for signs of my Ideas, to make them known to others not by any natural signification but a voluntary imposition, 'tis plain cheat and abuse when I make them stand sometimes for one thing

Dalgarno 1661, 1834. Sprat 1657, 1959: 111. ibid.: 113. Locke 1706, Book III, Chap. 2, Section 8; 1963, 2: 165.

18 and sometimes for another; the wilful doing whereof can be imputed to nothing but great Folly, or greater dishonesty."

Wilkins(1668, 1954: 17-18) stated: As for the ambiguity of words by reason of Metaphor and Phraseology, this is in all instituted languages so obvious and various, that it is needless to give any instances of it; every Language having some peculiar phrases belonging to it, which, if they were translated verbatim into another Tongue, would seem wild and insignificant ... And although the varieties of Phrases in Language may contribute to elegance and ornament of speech; yet, like other things of fashion, they are very changeable, every generation producing new ones ...

This quotation impairs the validity of Cohen's (1966) claim that at that time the meanings of words were universally seen as stable and unchangeable and that the process of language change was not at all recognised. In the seventeenth century the "instability" of modern languages was acknowledged (cf. Jones 1953: 263), and judged as one of the reasons for the inadequacy of language to express scientific truths. Hobbes (1651) provides the most complete and clear example of the epistemological basis for the empiricist attack on metaphor. He holds that speech consists of names that are connected by us so that we may record our thoughts, recall them in memory, and express them to others. One of the chief reasons for expressing our thoughts is to communicate our knowledge. This function is frustrated and impeded whenever we use words metaphorically; that is, in other sense than that they are ordained for; and thereby deceive others;24 Metaphors, and senseless and ambiguous words, are like ignus fatui; and reasoning upon them is wandering amongst innumerable absurdities; and their end, contention and sedition, or contempt.23

Hobbes then attacks speech that undermines proper reasoning and leads to absurd conclusions. Included in his displeasure is the use of metaphors, tropes, and other rhetorical figures, instead of words proper. For though it be lawful to say, for example in common speech, the way goeth, or leadeth hither or thither; the proverb says this or that, whereas ways cannot go, nor proverbs speak; yet in reckoning, and seeking of truth, such speeches are not to be admitted.2'

The dissatisfaction of philosophers with language, coupled with the realisation that it was unavoidable as the means of communication, inspired in them a desire to reduce language to its simplest terms, to make it as accurate, concrete, and clear an image of the material world as was possible ... Not content with reducing all physical phenomena to matter and motion, scientists desired to impose the limitations of the same terms upon language, since they believed that only by making language correspond more closely to the truths of nature was it possible to advance knowledge.27

Such ideas underlie the linguistic views of scientists in that period. They believed that the truth of the ideas about physical phenomena depended on the accuracy of the terms of language used to articulate them. Hence, they desired to oppose the natural trend of words 25 24 25 26 27

ibid.: Book III, Chap. X, Section 6; 1963, 2: 492-493. Hobbes: Leviathan, 1651, 1965, Part 1,4: 13. ibid.: 5: 22. ibid.: 21. Jones 1932: 320.

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to "fade in predicational use", by means of strict definitions, albeit they also at least partially realised that the definitions themselves may be faulty, since they are composed of words, and "those words beget others" (Bacon). Still, they hoped that it would be possible to reach the ideal state in which the words used would be exactly equivalent not to vague man-made conceptions reflected in the loose usage of the past, but to the objective truths of nature. The belief in the possibility of a "pure" language closely corresponding to "things as they are" found its expression in the attempts to devise a "universal character" and, later, a "universal language" for philosophical purposes. At first, the idea of a "universal character" amounted to the pursuit of a "modest" aim of devising a written language which, owing to exactness of its symbols, could be read in any natural language. The idea was inspired or at least supported by a newly acknowledged property of Chinese hieroglyphic writing: owing to their lexicographic nature, the Chinese writings could also be read in other languages considerably different from Chinese, such as Korean. Later, the taxonomic character of Chinese, in which multiple common nouns explicitly contain the names of their superordinate categories, contributed to setting the more ambitious goal of creating a "philosophical" language whose symbols would clearly display the actual divisions and relationships in nature, making it a perfectly suitable tool for scientific research. The tendency to see the world as easily subjectable to univocal, neat classification, making possible corresponding ordering of vocabulary used to refer to all phenomena, was displayed in attempts to develop artificial languages cleared of all the ambiguity and vagueness of words, that is to say, of all the connotations of past usage.28 One of the demands made on the language of science was that it should enable the user to construct technical taxonomies, and the designs of artificial language contained regular morphological patterns for representing clear-cut classification of words corresponding to clear-cut classification of reality. Also the remarkable development of mathematics in the 17th century and especially the improved mathematical symbols that were coming into use inspired the conceptions of scientific language. Scientists wished to reduce language to the same symbolism which has proved successful in mathematics, to re-make it out of symbols purified from useless connotations like the symbols of algebra. Ward (1654: 20-21, 1932: 322) praises the change from the traditional, language-based mathematical writing to the universal notations replacing symbols for words, and hopes that it would also be possible to use such a notation also for other things: ... and herein I was presently resolved that Symbols might be formed for every thing and notion. He believed that the universal character could be produced wherein all Nations might communicate together, just as they do in numbers and in species," sharing this view among others with Boyle (1647, 1965,1: 22) who claimed that ... since our arithmetical characters are understood by all the nations of Europe, though every several people express that comprehension with its own particular language, I conceive no impossibility, that opposes the doing that in words, that we see already done in numbers. Among scholars who published works containing either philosophical speculations concerning the universal character or a universal philosophical language, or the actual designs of such a language, were Newton, Leibniz, Wilkins, Hartlib, Dalgarno, Boyle, Ward, Bathurst, Wallis, Webster, Petty, Henry Edmunson, Cave Beck. Ward 1654: 21, 1932:323.

20 The idea of a philosophical language akin to mathematical notation culminated in the works of Leibniz, who sought to extend the domain of the cognitive use of signs from mere expression to philosophical reasoning and called for "characteristica universalis" which would be "eine Art Kalkül, der auf alle Gegenstände des vernünftigen Denkens anwendbar sein müsse"30 - a concept summed up in the well-known "Calculemus!", expressing a belief in the possibility of achieving a strict mathematical rigour in reasoning by means of Charaktere oder Zeichen, die geeignet wären, alle unsere Gedanken ebenso rein und streng auszudrücken, wie die Arithmetik die Zahlen oder die analytische Geometrie die Linien ausdrückt." The myth of Babel provided a further support for the belief in the possibility of a "language ... (where every word were a definition and contained the nature of the thing) [which] might not unjustly be termed a naturall Language, and would afford that which (has been) vainly sought for in Hebrew".32 Ward associated this "natural language" with the language Adam spoke in the garden of Eden, and believed that "if the design of Real Character take effect, it will in some part make amends to mankind for what their pride lost them at the tower of Babel"." In the eighteenth century, a somewhat different attitude to the question of the appropriateness of language use emerges, as represented by Euler, opposing the idea that it is necessary to purify the language of science from metaphorical terms of ordinary language. Euler (1769, letter 55; 1986: 61) seems not to mind them, under the condition, that the application of such terms does not make us blind to the "true cause" of the phenomena under description: Ihre Hochheit kennen die Eigenschaft des Magnets, daß er das Eisen an sich zieht; man sieht nämlich, daß kleine Stücke Eisen oder Stahl, z. B. Nadeln, wenn man sie in die Nähe eines Magnets bringt, mit desto größerer Gewalt... angezogen werden, je näher sie sind. Weil man nichts gewahr wird, was sie gegen den Magnet stieße; so sagt man, der Magnet ziehe sie an, und die Wirkung selbst Attraktion. Man kann indessen nicht zweifeln, daß es eine sehr feine obgleich unsichtbare Materie gebe, die diese Wirkung hervorbringt ... aber da unsere Sprache sich bloß nach dem sinnlichen Schein richtet, so ist man bei dem Ausdruck geblieben: der Magnet zieht das Eisen an sich. Our own time tends to be very critical of the early modern attitude to metaphor in the language of science, and to this period's idea of a philosophical language reform in general. This critical attitude sometimes comes close to the misunderstanding of the requirements which the anti-metaphorical (and, more generally, anti-rhetorical) language reform was to perform. The call for the relegation of metaphor from the language of science was motivated by the same set of goals which today form a generally accepted cornerstone of any scientific terminology, which is the prescription of a permanent assignment term-concept and elimination from it of homonymy, synonymy, quasi-synonymy, and polysemy (cf. Hoffman 1985: 28). According to Weisgerber (1954: 95ff.), the ideal of a specialist's language would be "völlige Übereinstimmung zwischen Wortfeld und Sachbereich". Moreover, the call for replacing natural languages with an artificial "natural" language embracing its domain in a taxonomic scheme finds its contemporary equivalent in the contemporary efforts in the field of the language standardisation for technical and scientific purposes. Today, one plans to 30 31 32 33

Brekle 1971: 142. Leibniz 1960, 1971: 142. Ward, 1932: 324. ibid.

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work out global terminologies (cf. ISO/R 860-1968) with the objective of reducing the differences between concepts and networks of concepts used in science in diverse languages. It is regarded as an achievable goal to develop multi-language terminological dictionaries where each concept would be assigned a classification symbol indicating its position in the system of concepts (cf. ISO/R 1149-1969). Such dictionaries would be ordered not alphabetically but according to the classification of concepts. The idea of a terminological thesaurus of this kind can be conceived of as a contemporary incorporation of the same methodological and linguistic postulates which, in the seventeenth century, culminated in the demand for "philosophical language".34 The error made by the reform-minded language philosophers of the seventeenth and eighteenth centuries seems to lie not so much in their call for a scientific language which would assign each concept a clear, univocal, complete meaning and a well-defined place in a system of concepts, free from metaphor and all the other deficiencies named above. After all, the same request motivates a great part of current terminological work. The error lay much more in the assumption that all words can be replaced by terms and all language can be replaced by terminology, so that natural language can be fully eliminated from the philosophical [scientific] discourse. That language depends on its dynamic properties such as ambiguity, vagueness and potential for metaphorical extension or transfer of names and meanings for its ability to accomodate newly discovered aspects of reality could hardly be recognised at the period when scientific terminologies - which would secure, at least for a time, some amount of stability in the use of language for scientific purposes necessary for efficient communication - were in a very early phase of development.

2.3. Metaphor, a friend of science: contemporary physicists on scientific language In spite of the specialisation and the division of labour between the scientist and the philosopher which took place between the "scientific revolution" of the 17th century and the present day, many contemporary practising physicists have taken it upon themselves to pontificate now and then on the nature and limits of their discipline, as well as on its language. Einstein, one of the "scientists turned philosophers", remarked that philosophy of science is far too important to allow the philosophers to take it over. One could rather legitimately claim that the term "philosophy of science" would be misused if applied to the physicist's reflection on his own branch of study; from the point of view of a professional philosopher of science, the physical scientist's comments do not keep track with the current state of the art (or the paradigms being currently in force) in the former's domain. Still, the simply worded "self-analysis" of the contemporary physicist with respect to the questions of language in general and its metaphoric aspects in particular lends itself to the purpose of conAn even stronger resemblance to the ideas of the early scientific language reformers is discernible in the complaint by Felber (1979: 26): "Standardization of terminology is well organized, both nationally and internationally. There is still the blame, however, that concepts, systems of concepts, definitions and terms, are standardized long after particular usage of terminology has been established ... It would save a lot of time if terminological research could be organized that way that competent institutions and organizations propose systems of concepts and the assignement of terms to concepts. Technical commitees and standardizing bodies could then concentrate upon the selection and prescription of concepts, systems of concepts, of definitions, and of terms."

22

trasting the present and the past views about the interface between metaphor, language and physical research just as well as the considerations of the philosophers do. Today, there is a growing consciousness that physics is not exactly what it was assumed to be in the nineteenth century and in Snow's "two worlds" hypothesis. It is much more a creative, fictional discourse influenced by the "spirit of the time" of which Heisenberg (1959: 109) said that it is probably a fact as objective as any fact in natural science, and this spirit brings out certain features of the world ...,

thus formulating an idea closely akin to what Fleck (1936, 1983: 126) expressed by saying: Der Denkstil erschafft die Wirklichkeit nicht anders als andere Produkte der Kultur und macht zugleich selbst gewisse harmonische Veränderungen durch. The physicists' view of language has greatly changed. The common-sense realism assuming that there is, or can be, a univocal correspondence between the terms of language and the phenomena to be described was considerably shaken by Einstein's theories of relativity which disclaimed the universal applicability of Euclidean geometry to the universe and countered the apparently unshakeable notion of universal time, that is, the applicability of the notion of simultaneity to events distant in space. In Heisenberg's (1959: 127) formulation, The philosophy of Kant... drew attention to the fact that the concepts of space and time belong to our relation to nature, not to nature itself; that we could not describe nature without using these concepts. Consequently, these concepts are 'a priori' in a certain sense, they are the condition for and not primarily the result of experience, and it was generally believed that they could not be touched by new experience. Therefore, the necessity of change appeared as a great surprise. It was the first time that the scientists learned how cautious they had to be in applying the concepts of everyday life to the refined experience of modern experimental science.

Einstein's theory of relativity showed that there is not only one valid geometry in which to describe the physical world, but many equivalent descriptions, either in terms of objects or light rays moving on straight lines unless deviating from them under the influence of external forces, or in terms of objects (and light) moving on geodetic lines following the space curvature at a given point. Two different languages can be used to describe one and the same set of phenomena, and the choice between them is made in most cases (that is, in all those cases in which the two descriptions result in the same practical predictions of experimental results) on arbitrary grounds. Obviously, Einstein's four-dimensional space-time continuum goes beyond the range of all languages based on the natural human forms of perception. The next blow for the realist's assumptions came with Bohr's (1928)35 notion of complementarity of the wave description and the corpuscular description of elementary particles. The principle of complementarity seems to violate the traditional and natural logic, in which if something is A then it cannot be B if A and B belong to mutually exclusive categories. Bohr and Heisenberg, the main authors and adherents of complementarity principle, accept dualism as an indication that there is no "true nature" of things to be looked for, and that doing physics is constructing imaginary models of reality incapable of objectivisation. This approach lets the semantic aspect of physical theory come to light: in the formulation of a physical question, the goal is no longer to grasp reality within a theory, but to analyse stateFirst presented in a slightly different version in Sept. 1927 at the International Congress of Physics at Como, Italy.

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ments as statements, signs as signs, and theory as a construction. What a physicist calls a particle (or wave) is defined through a whole complex of meanings; the word points to a system of linguistic terms of which it is an element. These systems, or semantic fields, are mutually exclusive entities, in the sense that the statements valid within one semantic field are not transferable to another: depending on what we want to assert, we switch from one system to another, without any bridging between the two which would allow us to say what, for example, an electron is in general, in a language neutral with respect to both complementary options. Bohr (1928) emphasizes that "every word in language refers to our ordinary perception", and according to our ordinary perception there are only two kinds of phenomena - corpuscular and undulatory. The physicist's awareness of this fact means awareness that the object of research is the structure of the possible conceptual construction rather than the objective given. Born (1969: 97) summed up the difficulty with the complementarity principle saying that its ultimate origin lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analysing visible motions it has developed two ways of representing them by elementary processes: moving particles and waves. There is no other way of giving a pictorial description of motions - we have to apply it even in the region of atomic processes, where classical physics breaks down.

The complementarity principle appears, then, as the consequence of the inability of language to encompass in a literal formulation the newly discovered aspects of physical objects, if we understand the notion "literal" in a way based on the assumption that there is a unique proper way of talking about things. The wave and particle languages are two ways to describe reality on equal footing with each other, none of them making any claims to being the proper, or more basic one, generally independent of the particular experimental arrangement. The question of "basicness" can only be judged on independent theoretical grounds, individually for each experimental arrangement. It is the occurrence of paradoxes such as the momentary (timeless) contraction of a wave to a point, violating the principle of the finite speed of physical processes, which leads to the exclusion of one set of notions (in this case, the wave language) from the description of "what happened" in favour of the other whenever such paradoxes threaten to occur. We may speak of the two languages as complementary "metaphorical redescriptions" of each other, where for each experiment the basic, or literal, description is the one which does not produce violations of theoretical assumptions. Thus, stretching the applicability of the scientific language to a whole range of new experiences by introducing two alternative perspectives from which to talk and reason about them, the complementarity principle enables us to deal with the physical world without abandoning the usual notions constituting the necessary means of communication. In the formulation by Bohr (1964, 1:26): Unter bestimmten einander ausschließenden Versuchsbedingungen gewonnene Aufschlüsse über das Verhalten eines und desselben Objektes können ... gemäß einer häufig in der Atomphysik angewandten Terminologie treffend als komplementär bezeichnet werden, da sie, obgleich ihre Beschreibung mit Hilfe alltäglicher Begriffe nicht zu einem einheitlichem Bilde zusammengefaßt

24 werden kann, doch jeder für sich gleich wesentliche Seiten der Gesamtheit aller Erfahrungen über das Objekt ausdrückt, die überhaupt in jenem Gebiet möglich sind.

The quantum theory widened the gap between language and the physicist's view of the world. In this region, the conceptual development of physical theory is unsupported by the existing language. The objects of physics today are much further removed from our concepts based ultimately on sensory experience than in the centuries past. Quantum physics put a question mark over the very concept of a thing. It made clear that language, the tool formed in the process of being applied to experiences which take place in the sphere of middle dimensions, is incapable of being stretched to directly describe the newly envisaged layers of reality in a way which would make sense to us; that is, without playing havoc with its semantics. Lightman (1984: 99) summarised these developments saying that "physics has galloped off into territories where our bodies cannot follow". Where bodies cannot follow, neither can language. It is only in the limiting case of large dimensions that the scheme of quantum mechanics becomes so close to classical physics as to allow us to use its language. The linguistic problem, however, is not eliminated through the large-scale interpretability of mathematical symbols: But the problems of language here are really serious. We wish to speak in some way about the structure of the atoms and not only about the 'facts' - the latter being, for instance, the black spots on a photographic plate or the water droplets in a cloud chamber. But we cannot speak about the atoms in ordinary language."

Still, it is impossible to describe any actual experiment without using ordinary language and the concepts of naive realism: Wie weit auch die Phänomene den Bereich klassischer physikalischer Erfahrung überschreiten mögen, die Darstellung aller Erfahrung muß in klassischen Begriffen erfolgen ..." [...] Als Ausgangspunkt müssen wir uns klarmachen, daß alle Kenntnisse anfänglich innerhalb eines der Beschreibung früherer Erfahrungen angepaßten begrifflichen Rahmens ausgedrückt werden muß und daß sich jeder solcher Rahmen mit der Zeit als zu eng erweisen kann, um neue Erfahrungen zu umfassen."

Complementarity helps transcend the gap between the old concepts and the new experience: ... die Entwicklung der Atomphysik hat uns gelehrt, wie es möglich ist, ohne die Umgangssprache zu verlassen, einen Rahmen zu schaffen, der für eine erschöpfende Beschreibung unserer Erfahrungen weit genug ist. "

The principle of complementarity juxtaposes representations, not "facts", and the representations can be talked of in "classical" language. Another practicing physicist, Lightman (1989: 99) comments upon the cognitive and communicative role of metaphors in physics admitting that Heisenberg 1959: 179. ibid.: 39. ibid.: 69. This does not need quantum physics to be noticed, even if it becomes particularly manifest in the context of the latter. In 1831, Goethe remarked: "Alle Sprachen sind aus menschlichen Empfindungen und Anschauungen entstanden. Wenn ... ein höherer Mensch über das geheime Wirken und Walten der Natur eine Ahnung und Einsicht gewinnt, so reicht seine ihm überlieferte Sprache nicht hin, um ein solches von menschlichen Dingen durchaus Fernliegendes auszudrücken." Goethe 1885, 3: 249. Heisenberg 1959: 89.

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ultimately, we are forced to understand all scientific discoveries in terms of the items from the daily life - spinning balls, waves in water, pendulums, weights on springs. We cannot avoid forming mental pictures when we try to grasp the meaning of our equations, and how can we picture what we have not seen? As Einstein said in the Meaning of Relativity, 'The universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of human body'... We find comfort in visualising an electron as a tiny ball, but we have also been shocked to discover that a single electron can spread out in ripples, like a water wave, occupying several places at once. We crave the certainty of our equations, but we must give names to the symbols. Lightman underestimates metaphor as it is used in everyday language, but there is correct insight in his claim (Lightman 1984: 101) that the essential difference between metaphors used inside and outside modern physical science lies in the degree of our knowledge of the primary subject in those two cases: When we hear that 'the chairman plodded through the discussion', we already know a good deal about chairmen, committees, and discussions. But when we say that a photon scattered off an electron, what concrete experience do we have with electrons or photons? From this, he draws the conclusion that in science, metaphors carry much greater a burden than in literature or history or art - "they must build their reality from the scratch". A somewhat different stand has been articulated by Max Bom, who has reflected upon the process of the extension of word meaning taking place whenever a concept in its original meaning turns out to be too narrow for our current purposes. The motivation for Bern's reflection on language in modern physics was Schrödinger's criticism of Bohr's notion of the dual nature of material particles (e.g. electrons), accepted rather widely among physicists by that time; Schrödinger challenges the current interpretation of the mathematical formalism and suggests a simple, monothematic "wave" picture. For Born (1953/54: 95), the question is of a linguistic nature and concerns the nature of word meanings: The difference of opinion appears only if a philosopher comes along and asks us: Now what do you really mean by your words, how can you speak about electrons to be sometimes particles, sometimes waves, and so on? Such questions about the real meanings of our words are just as important as the mathematical formalism. In what follows Born opposes Schrödinger's "extremist" standpoint denying any kind of "reality" to the notion of a particle. He postulates instead that the consequence of showing that these particles are not behaving as good, well bred particles, like a grain of sand, should behave,40 will be rather the change of meaning of "particle" than abandoning the notion altogether. He points to the process of meaning extension taking place in science, exemplifying it with the history of the concept of number. In answer to the criticism by Schrödinger, he maintains that the use of the concept of particles in contemporary physics has to be justified in just that way. The condition for such a process to take place is that it must share some (not in the least all) properties of the primitive idea of particle (to be part of matter in a bulk, of which it can be regarded as composed).41

40 41

Born 1953/54: 99. ibid.: 101.

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He says further, referring to Schrödinger's objection to the "particle", or "atom", hypothesis, that Schrödinger's examples seem to me of the kind which prohibited the Greeks from admitting the representation of the diagonal of the unit square as a number; it differs from all possible ratios of integer.42

Born recognises correctly that all our language, in life and science, is growing through generalisation of concepts, which sometimes are first considered to be 'as ifs', but then are amalgamated and become legitimate words in their own right.45

What he refers to in this remark is the same process of emergence and death of metaphor which linguists like Langer, Brown or Turbayne describe as the mechanism of language growth. This is, however, not the whole story about the use of the words in a quantum mechanical description. Physicists have learned to accept the fact that the only way to speak about things under study not immediately available to the senses is to speak of entities in "as ifs" - theoretical models - of which there can be many for a given system,44 and each of which includes some aspects of the system under study and excludes others.45 In this way, the complementarity principle has lost its aura of sensation and turned out to be just one of a host of cases in which the choice of one or another model, of one or another language, as the means to describe a particular situation depends on the specific requirements of this situation. The post-relativity developments in the physical methodology constitute a part in a shift of world view which took place in the present century, the shift of emphasis from the objective to the intersubjective aspect of the world picture, and it is only natural that they have found numerous parallels in the development of linguistics and cognitive science. Among other things, just as an non-Aristotelian, three-value logic was introduced in physics to make it possible to speak of "indeterminate" position of an electron neither being nor not being at a given point (Birkhoff, Neumann, later Reichenbach and von Weizsäcker), so Zadeh's logic defining, in addition to "true" and "false", an infinite range of intermediate values came to be admitted in cognitive semantics, e.g. as far as the questions of category membership are concerned. The necessity to apply a multi-valued logic which violates the rule of excluded middle hangs together with the contemporary tendency to see the observer

ibid.: 101-102. ibid.: 102. Cf, for example, a family tree of the models of the laser by Haken, H.: The Semiclassical and Quantum Theory of the Laser, in Cartwright 1983: 80. The generalisation of meanings of terms used to refer to the entities in the representation may take place nonetheless, as assumed by Bohr. Cf. section 7. 2. 2.; also Hütten (1958) on "oscillator". The question is roughly this: when we say "X supports my view", are we using the word "support" literally in a generalised sense, or metaphorically? The same concerns the words "wave", "particle", "oscillator" in their new senses. At other place, we use the formulation "speaking literally on the basis of a metaphorical model". A digital decision "earlier metaphor generalised into literal meaning, or metaphorical speaking?" is not so much at issue; it is more interesting to show on what basis such linguistic condition comes about. If we favour one or the other way of speaking somewhere else in the text, it is merely a linguistic option.

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and the act of observation as included in the object of reflection rather than separable from it. In linguistics, it means the renouncing of the Fregean definition of truth value implying truth judgements independent from the human factor. From the cognitive perspective, the possibility of univocal, human-independent and context-independent categorisation of entities and processes appears illusory. The criteria of categorisation of inanimate objects include, for example, such an evidently human, bodily-based factor as the similarity vs. difference of the motoric programme associated with their application. In a similar vein, modern physics gives up the idea of absolutely objective recognition in favour of a new picture in which the observer, or, more precisely, the fact of a measurement being taken, is included in the results of observation; the description of experimental results renders the whole complex consisting of the object, the instrument, and the act of observation. In Heisenberg's (1959: 58) famous formulation, physicists became aware that the object of physical research is "not nature in itself but nature exposed to our method of questioning"; the conceptual mind cannot grasp reality independent of human thought.

2.4. Current paradigms in the research on metaphor in science 2.4.1. Linguist's metaphor, philosopher's metaphor Science deals with new knowledge; it presents new aspects of reality which were previously unknown. For that reason, it also needs new means of representation and description, but they may only be derived from the old. This may be done by arbitrarily coupling a name originally denoting something else with a definition (catachresis), and by the extension of reference or transfer of existing concepts to cover new items of knowledge. The latter two processes - the extension and transfer of concepts - pertain to the process of concept formation in general, and the formation of theoretical concepts and structuring scientific theories in particular. The presence of the two aspects in the phenomenon of metaphor, the verbal and the conceptual, is reflected in the fact that its contribution to the discourse of physics has been approached from two different standpoints: that of a linguist and lexicologist on the one hand, and that of a philosopher and historian of science on the other. Whereas the former approach focuses on the role metaphor plays, as one of many means, in the growth of vocabulary including scientific terminology, the philosophy and historiography of science focus upon the theoretical-conceptual level; the notion of metaphor appears there in the context of the role played in the discourse of physics by analogical thinking and analogy-based models. The transfer of denotations on the one hand, and the conceptual structure-mapping by juxtaposition of two broader domains on the other, are the two corresponding senses in which the notion of metaphor is typically used in these two approaches. The phenomenon of transfer of denotations on the basis of such similarities - or other kinds of relatedness between the donor and the recipient subject which are inconsequential for physical theory, such as e.g. shape similarity or synesthesis, whereas within the scope of the linguist's domain, is of little interest for philosophers of science dealing with the subject of metaphor. The kind of metaphor which the historian and the philosopher of science are interested in are exceptional cognitive events in which a novel juxtaposition is created, restructuring a scientist's familiar conception of reality.

28 2.4.2. Philosopher's metaphor 2.4.2.1. True models, objective mathematics? In a comment on the modern physicist's view of the methods and aims of physical science, Wallace (1989) recollects a lecture in which the lecturer first informed the audience that he was going to convince them of the truth of the quantum field explanation of vacuum; however, all the experimental evidence cited was equally accounted for by the source theory, standing in direct opposition to quantum field theory. Asked about it, the lecturer admitted it to be the case and remarked that the choice among such incompatible theories is a matter of metaphysical predilection. The quantum explanation of vacuum is in no way an isolated example: rather, it is commonplace that "the facts of the situation do not pick out one right model to use,"4* and that the choice among available interpretations must be made on other grounds. A similar change has affected the relationship between mathematics and physics, which is seen very differently today than it used to be two hundred years ago, when the formal rigour of the former seemed to secure the objectivity of the latter. In the course of the preceding century, mathematics liberated itself from the expectations of "Anschaulichkeit", physical interpretability, and intuitive comprehension. Modern mathematics reformulated its selfdefinition as a free construction. This construction creates, rather than reflects that which exists; it defines existence by internal non-contradiction; it is an artificial language in the form of self-referring, self-sufficient system of rules; it is restricted only by its own rules rather than by any considerations external to it; it is no longer founded upon the number as the basic idea because counting is an operation, an act identifying and naming objects external to the system; it describes possible rather than the existing worlds; it produces methods rather than insights; it aims at thinking rather than knowing (cf. Mehrtens 1990). This reform of mathematics has alienated it from the natural sciences. Even if the "free constructs" of mathematics, created without any external (incarnated) interpretation in the background or any pretence to applicability, frequently turn out usable tools in physical calculations, the concept of the relationship between them has undergone a shift. If mathematics is all about thinking rather than about being, the fact that it can be successfully applied to the real world is even more of a mystery than it used to be before. Why are mathematical formulae, which relate signs to other meaningless signs, applicable in the physical domain? Where does the predictive power of mathematics in this domain come from? How are the processes of nature correlated with the processes of mathematical transformations? Mehrtens (1990) provides an answer of sorts: mathematics and its applicability have been worked out in the course of its historical development, for which the possibility of a nexus with the technical performance was prerequisite. Nature is not fully chaotic and can be re-constructed by a society as an ordered symbolic system. Mathematics is about the possibilities of transformations of symbolic structures, which makes it applicable to nature as such a man-made system. Western culture has chosen a calculable nature and has worked it out. Once we have found a perspective from which the mathematical character of nature appears as a "big choice" made by Western culture rather than a necessity, we are prepared Cartwright 1983: 104.

29 to see the actual practice of science as a practice of corresponding "small choices" (and the other way round). The role of mathematics in modern physics seems to be that of a repertoire of tools to choose from according to the requirements of the situation under study. Frequently, the same situation can be coupled with more than one mathematical description (usually via theoretical models). The ease of calculations, resulting from the individual preferences of the researcher as well as from the peculiarities of the case, decides which mathematics is chosen in a particular case under study whenever there are alternatives to choose from. This is similar to (and usually associated with) choosing from among a number of theoretical models, when choices must be made which are not "dictated by the facts". While Mehrtens (1990) focuses upon the "big choice" and points to the mathematical structure of nature as a decision made by Western societies, Cartwright (1983) starts at the other end of the problem and demonstrates that even if mathematics is rule-governed and nature partially orderly, the process of fitting the latter into the former in particular cases is not quite so rule-governed as usually assumed. Physicists, particularly in the applied physics and physical engineering (observe that it is the practical applications of science that make it successful and respectable!), do not work from theory to prediction to experimental corroboration or refutation. Rather, their job is to find a fit between the results and any of the theoretical models and mathematical descriptions that are at hand, if needed - using whatever approximations they can think of as justifiable on whatever grounds. One kind of approximation in physics fits the fundamental equations of theoretical models to the actually observed situations. It is not the case that the descriptions of situations under study are derived from the former. On the contrary, the fit between the experimental results and the mathematical formula is achieved through whatever approximation "correcting" the fundamental formula is needed to achieve it, such as, for example, the abandonment of some terms as negligible, or the replacement of a sum by an integral. (Of course, such approximations must be justifiable, but their justification is a post-factum undertaking.) Heuristics are used, for example, in the phenomenon known as the Lamb shift: the three approximations we use could be applied in any order, but only one order supplies the "correct" prediction which fits the experimental results, so this is the order in which we apply them. The decision is made on practical grounds, without any backing from the theory. In another kind of approximation, measurements of the relevant parameters are made in the actual situations (e. g. in transistor circuits) and then the measured values, rather than the theoretically predicted values, are used for further calculations applying to theoretical models. Such practical approximations improve on the accuracy of the fundamental laws, the doctored results being much closer to the facts than the outcomes implied by the laws. In any case, approximations "take us away from theory and each step away from theory moves us closer towards the truth",47 i.e., towards the actually observed results. In view of both the choice of a theoretical model and of a mathematical description being underdetermined by either theory or facts, the beliefs in the reality of theoretical models and in the objectivity of the associated mathematical description are severely shaken. The loosening of the sense of rigour customarily associated with the idea of mathematical description has contributed to the re-orientation of philosophers, who now look upon physics as a re-construction rather than a reflection of reality, and has promoted the interest in "nonrigorous" operations of mind in the context of making physics, with analogy and metaphor in the lead. 47

ibid.: 107.

30 2.4.2.2. Metaphor and physical theory Contemporary historian's and philosopher's of science perspective upon the role of metaphor in the physical discourse focuses upon the recognition that theories are model-structures and metaphors are used to provide interpretations of the elements in these structures. " In this view, All applications of a theory to experience involve the use of metaphors, since, in each case, the experimental phenomena are 'seen' in the light of certain models.49

For Kühn (1979: 415 ff.), the notion of metaphor refers to all these processes in which the juxtaposition either of terms or of concrete examples calls forth a network of similarities which help determine the way in which language attaches to the world ... Metaphor plays an essential role in establishing links between scientific language and the world. These links are not, however, given once and for all. Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature ... These alternations result in more effective ways of dealing with some aspects of some natural phenomena. They are thus substantive or cognitive.

Similarly, Arbib and Hesse (1986: 156) locate the notion of metaphor on the level of the conceptual networks shaped by cognition of similarities between two domains: Scientific data are initially described either in an Observation' language or in the language of a familiar theory and are then redescribed in terms of a theoretical model that allows two apparently disparate situations to interact in a novel way. For example, sound and waves on water are both parts of our everyday observation; what is novel is the suggestion that there is something about sound akin to waves - not the wetness or the sight of whitecaps but an underlying regularity of motion. We recognise some positive analogy between two systems, and the negative analogy creates a tension that can invest the phenomena with new meaning. Metaphor causes us to 'see' the phenomena differently and causes the meanings of terms that are relatively observational and literal in the original system to shift toward the metaphorical meaning. Terms such as 'harmony', 'resonance', 'pitch' come to be used with precise meanings derived from the wave model. Meaning is constituted by a network, and metaphor forces us to look at the intersections and interaction of different parts of the network. Metaphor, then, is a conceptual phenomenon pertaining to the construction of scientific theory, an indispensable instrument of thought, a hypothetical-like construct, which reclassifies and assesses the received view of things in terms of alternate properties.50 [...] From Newton's view of the solar system as terrestrial projectiles to Boyle's clock metaphor, the history of science is replete with those who have reformulated problematic concepts through metaphors ... 51 Metaphor is critical to science. Metaphor in science serves not just as a pedagogical device, like the cosmic balloon, but also as an aid to scientific discovery. In doing science, it is almost impossible 48

49 50

51

Kühn 1979: 415 ff.

Bradie 1984:237. Muscari 1988: 423.

ibid.: 425.

31 not to reason by physical analogy, not to form mental pictures, not to imagine balls bouncing and pendulums swinging. Metaphor is part of the process of science." Metaphors play an explanatory role in science providing means for a cognitively satisfying and theoretically fruitful redescription of the subject under investigation: Following Kühn, Giere, and others, the application of a theory to the world involves 'seeing' that a particular phenomenon can be modelled in a certain way ... On Kühn's (1960: 190) account, Bernoulli 'saw' the water flow as an exemplification of pendulum motion and was thereby able to use the Newtonian solution to the problem for the reservoir problem. This, I contend, is an instance of metaphorical redescription ... Thereafter, no one could claim to have a complete understanding of the phenomena without realising that it could be so conceptualised." Metaphors pertaining to scientific theory are scientific similes and analogies: That the metaphorical in science usually appears in similistic or analogical form should not be surprising; similes and analogies seem to assimilate the new to the old and therefore prevent fresh relationships from being unduly unfamiliar. Although it is highly questionable whether all similes and analogies are necessarily explicable in detail ... there is little doubt that such figures seem to supply a lend-lease of attributes which tend to bring the form of the unknown entity closer to the structure of the more established and principal subject. If predictable regularity and antecedent resemblances are measures for judging scientific theory, then similes and analogies would certainly appear to be the sort of metaphor that fits this criteria the best.. . M Considering metaphor in the context of its affinity with scientific models and analogies is a part of the philosopher's of science notion of metaphor as not confined to language but also pertaining to other levels of human cognitive grasp of reality: metaphor is both the site and means for exchanges among not only words and phrases, but also theories, frameworks, and ... discourses.55 2.4.3. The view of metaphor as the linguistic dimension of a scientific analogy Even if most philosophers of science writing on the subject represent a broad notion of metaphor, which includes scientific analogies, models, and visualisations among its sub-species, this position is not universally shared. Contrary to the approach defining metaphor broadly as including analogies and models, some scholars oppose the notion of metaphor on the one hand to the notions of model and analogy on the other as a linguistic versus extra-linguistic phenomenon. Harre (1960: 112-113) characterises metaphor as a linguistic expression. For Martin and Harre (1982: 96), metaphor is a figure of speech in which one entity or state or affairs is spoken of in terms which are seen as being appropriate to another. Similarly to the above quoted linguists, they define a metaphorical use of a term as a use which violates the subcategorial rules of the lexical items of a sentence.56

Lightman 1989: 97. Bradie 1984:235. Muscari 1988: 424. Bono 1990: 73. Martin and Harre 1982: 98.

32 The difference between a metaphor and model is characterised as the difference between a figure of speech and a non-linguistic analogue: ... if we use the image of a fluid to explicate the supposed action of the electrical action of the electrical energy, we say that the fluid is functioning as a model for our conception of electricity. If, however, we then go on to speak of the "rate of flow" of an "electrical current", we are using metaphorical language based on the fluid model."

The relation between model as a conceptual structure and metaphor as a verbal phenomenon is further specified: The model gives rise to, 'spins off' a matrix of terminology which can then be used by the theorist as a probative tool. Speaking metaphorically on the basis of a model, a scientist is enabled not only to posit but to refer to theoretical entities by the use of terms which transcendent experience in that their semantic context is not fully determined a priori by the empirical conditions for their applications.58

For Dreistadt (1968: 97), metaphor is "an analogy expressed in verbal form", while "an analogy is in the form of sensory, usually visual, imagery". 2.4.4. Our approach: a preliminary note From what has been said before, it is evident that we shall not use the notion of metaphor in a sense restricted to the level of word meanings and verbal expressions, neither will we identify a metaphor in science with an analogy-based theoretical model. We assume that it makes sense to talk of the contribution of metaphors as conceptual phenomena distinct from analogical models to scientific theorising. In what follows we also want to have a look at such aspects of metaphorical thought and language of science which usually escape notice when its focus of attention centers upon analogical models. To be able to identify them, we first treat in more detail the relation between metaphors and models, as well as between metaphors and false hypotheses over-estimating the similarities between two kinds of physical processes.

3. Identifying metaphor in physical science: sorts, functions, and related concepts Because the current proliferation of approaches to metaphor mentioned in the first section makes it increasingly difficult to treat the notion itself as given, we need to give it some sort of definition to start with in order to identify what qualifies as metaphor in physics. As the conceptual facet of metaphor makes it a member of a family of notions including scientific model and analogy, in order to delimit the concept of metaphor we shall proceed by giving an account of the relationship between metaphor and its related notions. We shall characterise the relationship between metaphor and the scientific model, and that between metaphor and what often counts as metaphor in the literature on that subject - an obsolete scientific theory based on overstatement of analogy. " ibid.: 100. 58 ibid.: 102.

33 From this, we proceed to a brief summarising definition of metaphor pointing out the distinction and the relationships between its linguistic and conceptual aspects, preliminary to characterising in more detail and subcategorising the two kinds of metaphors in terms appropriate to each of them. To arrange the samples of physicists' metaphors, several alternative criteria of categorisation could be applied. After specifying the available alternatives and identifying the ones we have chosen to apply, we proceed to characterise various sorts and functions of metaphor in the physical discourse.

3.1. Metaphor and related concepts The bulk of the current literature on metaphor in the exact sciences represents the perspective of a philosopher of science rather than that of a linguist. Scientific metaphors are linked to concept formation, scientific explanation, theoretical confirmation, and scientific models, all of which are the philosopher's of science issue. The present-day philosophical discussion of metaphor in science in general, and in physical science in particular, takes place in the wider context of the discussion of the role of models and analogies in scientific discourse, where it partially merges with these other notions. This happens as a result of the current abandonment of the traditional, Aristotelian view of metaphor as transfer of denotation from its proper set of referents to another, reformulated more recently (in a critical vein) into a purposefully over-simplifying phrase "saying one thing and meaning another", which treated metaphor as a matter of words and left out of focus the underlying, cognitive, conceptual aspects of metaphor. On the other hand, the presently more current notion of metaphor, which emphasises its conceptual aspect, expressing it in terms of the donor subject and the recipient subject and the transfer of conceptual structure between them, tends to make "metaphor" either into a non-scientific equivalent of a scientific analogy, or to a superordinate category including among its subcategories literary metaphors, scientific models and analogies, and false scientific hypothesis based on overgeneralised analogies. The prevailing mode of the contemporary reflection upon metaphor in physics has been determined by the fact that this latter "cognitive" definition of metaphor hardly offers a clearcut principle of differentiation between scientific models based on analogies on the one hand, and other types of science-relevant metaphorical processes or concepts on the other. Theoretical models based on analogies are obviously essential to the physical research, so such a broad notion of metaphor leads to all the emphasis falling upon the model-theoretical aspect of metaphorical processes, actually reducing (or broadening) the question of metaphor in physics to the question of the role played in its theories by analogy-based models. In our analysis we want to focus not upon the metaphorical aspects of physical models based on analogies but rather on these aspects of metaphor in science which are not fully exhausted by the analysis of such models. To be able to identify the functions of metaphor in physics which are not identical with that of analogical models, we first have a close look at the relationship between models and metaphors (section 3. 1. 1.). A further, independent step in our analysis of metaphor in physics will be reducing the scope of this notion through identifying the "as if" aspect as a central characteristic of metaphor. Such a step excludes certain classes of scientific models from the species of metaphor.

34

These are false hypotheses based on factual assumptions, grouping physical phenomena in ways which did not stand up to critical investigation and had to be eliminated in view of later discoveries (section 3. 1. 2.). We argue against calling models of this kind metaphors at the stage at which they claimed reality status. We recognise, though, that such false hypotheses are not irrelevant to the question of metaphorical processes in physics. Some of the concepts applied in them have not been simply thrown away, but have been retained in physics undergoing a necessary change of meaning. We regard it as a metaphorical process because it fulfills the criteria in terms of which we define metaphor: transfer or extension of a concept to a kind of referents which violate certain important semantic restrictions on the literal (usual) application of this concept. We call this kind of metaphorical process "assimilative metaphor" because a concept "assimilates" to the changes of knowledge about its referents, contrary to what happens in the more common "stipulative" metaphor consisting in a sudden production of new meaning. The assimilative metaphor will be illustrated in chapter 7. 3.1.1. Metaphor and model 3.1.1.1. Scientific model: an outline Hütten (1958) is certainly wrong to claim that the word "model" originally meant an architectonic blue-print and entered the language of physics in the nineteenth century. Digges (1576) uses the word to refer to the Copernican cosmological model; Bacon (1605, 1990: 517) speaks of "the ancient opinion that Man was Microcosm, an abstract or model of the world"; and also Sprat uses it in a quite contemporary way in "The History of the Royal Society of London", 1657. In the meantime, the word has fallen victim to the process of "fading in predicational use". The analysis of the relation between the notions "model" and "metaphor" is made difficult by the fact that not only the notion of metaphor, but also that of a model is understood and applied differently by different authors. We apply it today to refer to such different entities as theoretical schemes, material constructions, mental images, physical processes, symbolic representations such as diagrams and computer programs, as well as to sets of mathematical formulae (mathematical models). The physicists of the Victorian epoch gave the name "model" to the mechanical constructions, constructed either in reality or only in the researcher's mind, which helped to conceptually embrace and analyse the behaviour of the system under study. The description of this function of models already implies a similarity to metaphor. What was sought was the conceptual and verbal access to new domains of study, and mechanics was applied for this purpose as the simplest theory at hand by means of which it was possible to interpret e.g. the electromagnetic phenomena: The model, then, was originally used for interpreting one theory, e.g. electromagnetism, in terms of a simple, or at least better known, theory, e.g. mechanics."

According to Hesse (1953/54: 199), If a hypothesis is to be a useful instrument of further research ... [it] should be capable of being thought about, modified and generalised, without necessary reference to experiments, so that it can " Hütten 1958: 83.

35 be used to predict future experience ... This ... condition is fulfilled in the case of the mechanical hypothesis typical of nineteenth-century physics, because they are expressed in terms of mechanical models whose behaviour is known apart from the experimental facts to be explained, (emphasis HP)

The function of models, then, is to lend themselves to manipulation according to familiar rules independent from the object under study, through which they can, if successful, become a source of predictions about the behaviour of the modelled system. To speak consistently about the similarities and differences between models and metaphors, it is necessary to reduce the meaning spectrum of the word "model" to exclude material devices, diagrams and computer programs as well as mathematical models. The comparison is confined to theoretical models, conceptual structures interpreting the mathematical descriptions of systems under study, by means of which we try to grasp such features of these systems which appear relevant to the knowledge about (the predictability of) their behaviour. The current applications of the word "model" are to be categorised into "model for" and "model of". "Model for" refers to what is also known as "parent situation" and "imported analogue". In this sense, the solar system is a model for Bohr's atom and a container with billiard balls is a model for the kinetic theory of gas. The notion of "model of" breaks down into: - the sense with which the word is actually used in physical research: the hypothetical structure created on the basis of "model for", which becomes attributed to the object under study; it contains only some of the properties of "model for" and leaves out other properties of "model for" as irrelevant to the description of the situation modelled. For example, Bohr's model of an atom abstracts from the size and the chemical composition of the planets and the sun, and the kinetic theory of gas does not attribute colour, nor a property analogous to it, to gas molecules, although colour belongs to the properties of the billiard balls in "model for"; - the philosopher's of science sense, following Hesse (1966): such a model contains the whole of the donor subject and the recipient subject, with the specified fields of similarity, difference, and the rest of which nothing is known as yet with respect to similarity. In what follows we will use the word "model" to refer to "model of" rather than "model for", and which of the two possible senses of "model of" is meant will be specified by the context. 3.1.1.2. Models and metaphors: affinities The affinity between both has frequently been pointed out by philosophers of science and of language. According to Hütten (1953/54: 289), We are forced to employ models when, for one reason or another, we cannot give a direct and complete description in the language we normally use. Ordinarily, when words fail us, we have recourse to analogy and metaphor. The model functions as a more general kind of metaphor.

In Hütten (1958: 83-84), he formulates this idea more precisely: The model is ... an incomplete, or partial, interpretation of one theory in terms of another, or of one theory in terms of simpler concepts ... Apart form the heuristic, or pragmatic, use the model has a logical function which remains indispensable, that is, an interpretation of a theory in simpler terms.

36 Models thus resemble metaphors in ordinary language ... When words normally used in a given context seem to fail, we seek help through words which, usually, belong to another context. In this way we extend the usage of our customary expressions; and this is necessary if we want to build up a technical language for describing an experiment artificially produced in the laboratory. In physics, we speak of a field offeree, or of the flow of heat, and so on. Indeed, technical discourse cannot do without metaphorical language ... The model arises from the simplest experience in the description of which the expression in question is used. This sets the standard, or is taken as a scheme of some sort, and so it prescribes implicitly the semantic rules for the usage of the expression.60 Black (1962: 236), too, notices similarities in the functioning of metaphors and scientific models: Certainly there is some similarity between the use of a model and the use of a metaphor - perhaps we should say, of a sustained and systematic metaphor. *' This line of thought is continued in Black (1979: 31): I am now impressed, as I was insufficiently so when composing 'Metaphor', by the tight connections between the notions of models and metaphors. Every implication-complex supported by a metaphor's secondary subject, I now think, is a model of the ascriptions imputed to the primary subject: every metaphor is a tip of a submerged model. The contemporary views concerning the similarity between metaphors and models can be summarised as follows: It is a function of metaphors as well as models to make the less known object of reflection graspable in terms of the better known and understood. This function is realised by conceptual transfer of relations and attributes from one domain to the other, which makes the latter conceptually and linguistically accessible or offers some advantages with respect to the conceptual and linguistic accessibility compared to other, earlier modes of description. Metaphors and models contain two domains: explanans (donor domain, secondary system, subsidiary subject, imported analogue), which provides the lexis and the rules of conceptual and linguistic (in a model, also mathematical) manipulation, and explanandum (recipient domain, primary system, principal subject, topic analogue), to which linguistic expressions and conceptual and semantic (and mathematical) rules become applied. Through the recourse to the explanans a description or re-description of the explanandum is created, which can be characterised as a partial interpretation of the latter; it is partial because it only pertains to those of its properties which are understandable - conceptually and linguistically accessible - by means of having correlates in the corresponding properties of the explanans. Numerous authors point out that conceptual metaphors as well as models can be subject to misinterpretation consisting in the loss, on the part of the human subject, of the ability to differentiate between the object of reflection and its metaphorical representation: There is always the danger that we take the model as the thing or situation for which it is a model." Turbayne (1970: XIV) claims that A metaphor which is used for purpose of illustration or explanation may become a model ... and when it does, there are definite disadvantages to be gained from taking it literally. For example, to 60 61 62

Hütten 1958: 83-84. Black 1962: 236. Hütten 1958: 83.

37 take as literally true one of the numerous models which occur in science would be to attribute the model to the world. It would be to say, in effect, that the world 'really is that way'. But this is not a useful way to approach either the world, knowledge, or science. It is not because it minimises the possibility of employing other models to illustrate the facts in question.

A similar thought has been expressed by Lakoff and Johnson (1980) with respect to metaphor - for example, the metaphor "labour is a resource", which makes the notion of work applicable in economic theories, "masks" other, human, dimensions of the process of work. As far as the "truth value" of models is concerned, we must refrain here from reconstructing the discussion between the "realists" and "instrumentalists" with respect to modeltheoretical structures and can only remark briefly that the status of models as "real", true or false representations of things modelled is affirmed by the latter. In the alternative view, models are not "true" or "false" but appropriate or not appropriate; the same property has been frequently emphasised with respect to metaphor. 3.1.1.3. Models and metaphors: distinctions It follows from what has been said above that the aspect of metaphor in view of which it can be compared to a model is the conceptual aspect, and that the proper candidates for such a comparison are extended metaphors, secondarily expressed in language. Obviously, there are differences between the scientific models and metaphors as they appear in literature and everyday thought and language. Hesse (1966: 168-169) analyses the differences between the literary metaphors and models: ... it is characteristic of good poetic metaphor that the images introduced are initially striking and unexpected ... that they are meant to be entertained and savoured for a moment and not analysed in pedantic detail nor stretched to radically new situations; and they may immediately give place to other metaphors referring to the same subject matter which are formally contradictory, and in which the contradictions are an essential part of the total metaphoric impact... Scientific models ... may initially be unexpected, but it is not their chief aim to shock; they are meant to be exploited energetically and often in extreme quantitative detail ... they are meant to be internally tightly knit by logical and causal interrelations; and if two models of the same primary system are found to be mutually inconsistent, this is not taken (pace the complementary interpretation of quantum physics) to enhance their effectiveness but rather as a challenge to reconcile them by mutual modification or to refute one of them ... literary metaphors, however adequate and successful in their own terms, are from the point of view of potential logical consistency and extendibility often (not always) intentionally imperfect.

Briefly, the differences between the metaphors in literature and everyday language on the one hand and the scientific models on the other are the upshot of the uses we put them to and the expectations they must fulfil in the respective domain of their application: The more precise or specific, and the more generative a representation is, the more willing one might be to call it a model."

65

Hoffman 1985: 348.

38 According to Gentner (1982), models - "explanatory analogies" - are structure-mappings meeting the criteria of systematicity, clarity, abstractness, and base specificity" to a larger degree than "expressive analogies" - literary metaphors. Another characteristic is the "richness" of analogy, that is, the amount of structure transfer. The scrutiny with which the potentially successful scientific models are analysed in order to establish the scope of correlation between their two subjects leads to mappings which typically provide a relatively rich structural analogy, otherwise the secondary subject does not qualify at all as a model for the primary subject. Another obvious difference pertains to the mathematical level of description, absent in the notion of metaphor. Hoffman (1985: 348) remarks that Substantive and symbolic models can do things - they behave or produce measurable events or symbols or numbers ...

A model in natural sciences is, prototypically, describable in mathematical terms; a model allows us to set forth a mathematical formula directly referring to the terms and relations within the model and indirectly, through the mediation of the latter, to the observables (experimental results), i. e. things and processes represented in the model. It is a function of models to let us test hypotheses and theories by delivering precise numerical predictions comparable with the results of measurements obtained. The verification of theoretical statements consists of this comparison. In this way, a model functions as a connecting link between theory and experiment. The value of a model is that it allows the mathematical formulae applicable in the secondary domain to be used in the primary one. The condition for this applicability of models is the clarity, that is, the unequivocality, of the structure-mapping. A model specifies which elements and relations in the domain of explanans are excluded from the transfer, and which are mapped onto the domain of explanandum, and the mapping is non-ambiguous (one-to-one). In addition to these sets, which are called positive and negative analogies (Hesse 1966), there is a field of "neutral analogy": it is a field of a potential extension of the model, that is, its elements can enter the field of positive analogy as a result of further research, and in this way it is a potential source of further theoretical insight. In contrast to this, in an imaginative poetic metaphor, the boundary between the positive and the neutral analogy is not unambiguously and interpersonally set down; the scope of the transfer and the consequent interpretability of the linguistic expression of a metaphor depend to a large extent on the imagination of the language users. Similarly, the underlying metaphors of everyday language contain parts of structure which are conventionally utilised and even lexicalised, but any parts of the structure of explanans (donor domain) are potentially available any time for the purpose of the generation of novel correspondences and transfer upon the explanans (recipient domain) (cf. Lakoff and Johnson 1980). When the notion of metaphor appears in the context of scientific research, it is sometimes used in a sense which includes scientific model (cf. section 2. 4. 2.), but frequently enough Systemacity is "the degree to which the predicates imported belong to a mutually constraining conceptual system"; "a mapping is systematic to the degree that any given predicate can be derived or at least partly constrained by the others. Higher-order relations that link lower-order relations are crucial to systematicity." Gentner 1982: 114. "Clarity" means clarity concerning which relations are mapped on to the target and which elements of the base are mapped to which elements of the target. Base specificity is the degree to which the structure of the base is explicitely understood (analysed).

39

it is applied in contrast to the latter and more or less implicitly assigned a "natural place" outside the exact sciences. For example, Black (1962: 238-239) states: Use of theoretical models resembles the use of metaphors in requiring an analogical transfer of vocabulary. Metaphor and model-making reveal new relationships; both are attempts to pour new contents into old bottles. But a metaphor operates largely with commonplace implications. You need only proverbial knowledge, as it were, to have your metaphor understood; but the maker of a scientific knowledge must have prior control of a well-knit scientific theory ... Systematic complexity of the source of the model and capacity for analogical development are of the essence.

This and similar remarks imply the view that the "natural" domain of metaphor, as opposed to a model, is the non-scientific, while suggesting at the same time that a model is a "metaphor-like" phenomenon that comes to play a role at mature stages of theory development where the standards of clarity and accuracy must be met. The metaphorical aspect of science is its model-theoretical aspect; a model is a "sort-of-metaphor" fulfilling the specific criteria of scientific theorising. If we assume that models in science are equivalents of metaphors in common and literary language and thought, it would seem advisable to restrict the use of the term "metaphor" to the latter domain; and, after paying due tribute to the recognised similarities between metaphors and models, to speak of metaphors while talking about everyday language and literature and of models while talking about scientific theorising. Gentner (1985) chooses this option and uses the notion of an "analogue" to refer to the superordinate category including both. However, some authors on the subject claim that both metaphors and models play a role in the scientific theory. Although there seems to be a broad consensus concerning the similarities between models and metaphors, as well as the difference between metaphors of everyday and literary language on the one hand, and the scientific models on the other, it is rather more difficult to draw a demarcation line between models and metaphors in natural sciences, as their precise differentiation is missing from the accounts claiming a role for one or the other or both in this domain. To give one example from many, in one of the most frequently mentioned works on metaphor in science, Hesse (1966) speaks in a rather undifferentiated way about "scientific models and metaphors". Hoffman (1985: 345) states: There is general agreement that metaphors and models differ and that different types of models can be distinguished. Yet, there is also agreement that metaphors and models serve many of the same functions in science, that models (as well as metaphors) serve are necessary to generate new predictions and explanations, since logical theories alone cannot lead to philosophically interesting questions and falsifiable hypothesis about causes and mechanisms.

but does not provide any clue concerning the criteria by which the models can be distinguished from metaphors. Commenting on Duhem, he says: He argued that models and metaphors (such as solar systems, onions, clouds, and glue balls as metaphors for atomic structure) were only memory mnemonics ..."

The feature which distinguishes modern science from its earlier stages is that today the donor domains for physical theoretical models can only come themselves from the domain of the physical, being typically another branch of physics; e.g., hylopsychic or organistic systems of concepts do not qualify as potential donor domains for physical models. If we make it the criterion for qualifying something as a model, such explanations appearing in the earlier 65

Hoffman 1985: 335.

40 stages of science are to be classified with metaphors but not with models. However, this exclusion of certain kinds of transfer from the class of models does not in itself provide a criterion for fully differentiating metaphors and models because it does not imply that all transfers from the physical to the physical are to be grouped with models rather than metaphors. It has sometimes been proposed that it is the simplicity or common character of the donor subject which could serve as the criterion for the differentiation between metaphors and models. Contrary to this view, Leatherdale (1974: 42) insists that the notion of "model" is actually used to refer also to less complex and systematic analogues: Since there is no clear-cut criterion by which to specify the necessary degree of complexity or system, and since some writers specifically include simple analogues drawn from ordinary experience in their discussion of models, there seems to be no special reason to insist on models being systematic analogues drawn from the existing science ... there is nothing which would in principle exclude simple analogues drawn from ordinary experience being subjected to the same analysis or discussion. Moreover, such an exclusion would create a discontinuity between early and later stages of science, and further would preclude consideration of at least some of the examples which are generally regarded as models in the literature.

On the other hand, it is frequently assumed that models are based on metaphors, in the sense that A model is an expression of a metaphor in that the model has a topic ... and a vehicle ..." Turbayne (1975: 229), too, holds that a metaphor is a potential source of a later model: The metaphorical merit of utterances, and the features which distinguish metaphor from non-sense should be analysable in terms of the models to which they give rise: a good metaphor is one which can be extended to a good model. At this point we can only remark briefly that we agree with the view that models are based on metaphors, and postpone more detailed consideration of this point till the next section. There are, then, at least three alternative definitions of the relationship between metaphors and models: superordinate category: metaphor: everyday language literature

ANALOGY model: science

superordinate category: METAPHOR non-scientific: scientific: metaphors of general language theoretical models literary metaphors superordinate category: METAPHOR non-scientific: scientific: metaphors of general language basis of theoretical models literary metaphors 66

Hoffman 1985: 347.

41

Summing up, the present-day discussion on the subject is inconclusive with regard to the question whether the relation between metaphors and models is that between a subordinate and superordinate category, or members of the same superordinate category distinguished by their respective fields of application; and although it is frequently assumed that models stem from or are extensions of metaphors, this assumption is hardly given a detailed exposition. 3.1.1.4. Metaphors turned models Our view about the relationship between models and metaphors, and in particular the sense in which models are based on, or develop out of, extended metaphors, is based on Ortony's (1975) idea of metaphor as a phenomenon which, speaking in terms of Gentner (1982), does not fulfil the criteria of a model: systematicity and clarity of the correspondences, and base specificity. Although the way to reflect on the contribution of metaphor to scientific theorising seems to lead through the componential analysis of the transfer, that is, the analysis in terms of a distinct, clearly delineated set of properties predicated on the recipient subject via the mediation of the donor subject, generally we do not regard metaphors as capable of being translated without loss of cognitive contents into such a list of properties. Numerous authors, beginning with Black (1965), point out that the essential feature making metaphors an indispensable means of thought and communication is the fact that their cognitive content cannot be fully grasped by such means. Ortony (1975) formulated this insight as an "inexpressibility thesis". According to him, what we perceive as our environment is continuous reality, whereas the role of reason and language is to convert this continuous experience into discrete segments. Today, it has been recognised that words have no sharply delineated meanings, and that the range of applicability of a word is fuzzy. In Ortony's view, the need to cover the continuous experience with discretised language necessitates the use of metaphor. An adequate representation cannot be achieved in each case by literal means, where each word straightforwardly contributes a certain portion of its meaning to the meaning of the utterance; the continuous nature of experience prevents language from having distinctions in word meanings capable of capturing every possible detail one might wish to convey. Metaphor makes up for this deficiency. All comprehension involves "particularisation": forming a mental image of what has been spoken about on the basis of world knowledge. The message must not explicitly give all the details. This particularisation in the hearer is a process contrary to what the speaker is doing while breaking his message into discrete segments of language: it is a "digitalto-analogue converter".67 The function of metaphor is to constrain and direct particularisation. It is not only more concise than a straightforward predication, but also less specific: unnameable characteristics are included. (We may often translate them into more literal expressions, but these are often just common metaphors.) The set of characteristics that is transferred from the donor subject to the recipient subject is a The notion of conversion of information from analogue (for example, pictorial) form to digital (for example, linguistic) form, necessarily accompanied by the loss of some information, has been elaborated upon on similar lines by Dretske 1981. A digital signal carries the information that a is χ without any additional information about a beyond its being x; the information carried by a signal in analogue form is always more specific. The conversion of the analogue sensorial information into digital form, prerequisite to categorisation judgements, is for Dretske the essence of cognitive activity.

42 continuum of cognitive and perceptual characteristics with a few slices removed rather than a list of discrete attributes.68

These "chunks of characteristics" are predicated en masse and bear a more direct relationship to cognition and perception than literal language because they have not themselves been internally discretised: metaphorical conceptualisation and language are characterised by a greater proximity to the experience of reality. Thus, a linguistic expression of a metaphor eliminates to some extent the step of "digital-to-analogue" conversion from an utterance to the particularised comprehension. Ortony's view implies the rejection of the "atomist" theory of meaning and comprehension assuming the inventory of fixed, contextually invariant set of semantic primitives as the building blocks of mental representation and the basis of comprehension. However, his metaphor of analogue-to-digital conversion does not make an explicit proposal for the format in which experience is represented in humans. If the internal representation is not in the form of discrete components corresponding to semantic components of lexical items, what does it consist of ? In cognitive psychology, several proposals have been made asserting that knowledge is stored partially in the imagistic form. In Paivio (1971, 1985: 141), images and verbal processes are viewed as alternative coding systems, or modes of symbolic representation, which are developmentally linked to experiences with concrete subjects and events as well as with language ... Chains of symbolic transformations can occur involving either words or images, or both ...

Kosslyn (1980, 1985: 143) maintains that mental representation is partly in the form of images; it contains a "propositional" component, and what he calls a "literal memory component" (it follows from his presentation that by "literal" he means "closer to the immediate experience"): The literal memory component contains representations that underlie the quasi-pictorial experience of imaging; they produce an internal depiction of the appearance of an object or scene.

The view that intuitions or judgements of similarity (and, hence, mental representations of things compared) can be holistic ("analogue") and do not necessarily involve breaking the domains of comparison into a list of specifications finds some support from the cognitive research done in a different context, that of prototypes and categorisation judgements, of Rosch and colleagues (1978). Indurkhya (1991: 24-25) links metaphor with the issue of categorisation on lines similar to Ortony's, applying the notions of crossing categories and a loss of information involved in transgression from perception to categorisation: Cognition typically involves grouping. Various objects and transformations, in the world that is made available to us by our perceptual and motor apparatus, are further grouped into categories and operations. Thus, the world that is seen from the cognitive layers is considerably more simplified and structured than the one seen from the lower perceptual layers. This simplification is necessary to make us survive in an infinitely complex Ding an sich with our finite and limited minds. However, an act of grouping invariably involves loss of information ... When a bunch of objects are placed in a category, their individual differences are overlooked; one might say that they are lost

68

Ortony 1975: 50.

43 by the process of cognition. Similarly, in putting two objects in different categories, their common features are lost as well. In grouping the world in one way ... the subject is deprived of a horde of alternate world views. If the cognitive relations between all layers were predetermined for each cognitive agent - whether biologically or culturally - then the lost worlds are lost forever ... The cognitive agent can never recover the information lost in cognition and reorganize its worlds views. However, if the cognitive agent can project different models onto the same environment, it can partially recover these lost worlds. Some of the distinctions between different parts of the environment that are lost as a result of the groupings induced on it by its conventional model69... can be made visible again under the 'regrouping' induced by another model. Thus, projective metaphor allows the subject to partially reclaim the loss of information that inevitably results froro cognition.

Beck (1978) characterizes metaphors as a mediator between semantic and analogue modes of thought and argues that apart from the verbal level of cognitive representation with its neat categories of objects, there is the imagistic, or sensory, level on which "images ... do not form neat categories; instead, they tend to ascent verbal norms"."Metaphors cross over such categorical divides as animate/inanimate, cosmic/biological, human/animal by recourse to associative and sensory logic" which "entails a movement from abstract to concrete", "thus bridging the logical gaps that separate object categories at the linguistic level".70 They "provide for movement between partial and abstract principles employed on a verbal plane and concrete, sensual, holistic images that thrive on a nonverbal one."71 On the other hand, Verbrugge and McCarrel (1977) characterise the ground of metaphor in terms of abstract relations of prepositional rather than imagistic nature. Also for them, however, these relations, constituting contextually determined similarities, are hardly reducable to a set of semantic primitives or intersections of existing semantic categories.72 We accept Ortony's definition of metaphor as a holistic juxtaposition of two domains not exhaustively analysed into discrete components, producing an intimation of similarity. At the same time, we can hardly think of any other way of systematically analysing particular cases of metaphorical transfer than by breaking it into such a list of prepositional specifications (a kind of componential analysis of meaning, although not necessarily in terms of semantic primitives): this is an unavoidable step in proceeding from an "analogue" phenomenon to its "discretised" representation in language kept as far as possible to the literal mode. Similar to our view is that of MacCormac (1985) who believes that not all the parts of a mental image can be reduced to propositions (linguistic representations), but there is enough to allow us to explain the comprehension of metaphor in semantic terms: images possess sufficient propositional content to be translated into semantic terms. We think that the difference must be kept in mind between the metaphorical process or "what actually goes on in the brain" when we comprehend or produce a metaphor, and an explanatory account that justifies it. The treatment in terms of componential analysis of the semantic structure belongs to the latter, and it may involve a translation of a partly imagistic representation into a verbalised, semantic representation.

That is, by a "literal" representation. Beck 1978: 85. ibid.: 86. Their example of such an abstract relation is the resemblance between tree trunks and strews in the context of the function of providing water to branches and leaves: "hollow pipes conducting a fluid to where it is needed".

44 In what follows we argue that the act of translation referred to above is similar to the process in which a metaphor turns into a scientific model. The point which we want to make with respect to the relationship between metaphors and models is that it is through being broken into discrete segments (specified properties) that particular metaphors become instrumental in theory construction. Metaphors become skeletonised into models by a process of growing clearness about the scope of the analogy between two domains and the correspondences between their structural elements. We have said that scientific analogues are characterised by greater clearness than metaphors: it is known exactly which elements and relations between them are seen as analogical, and this aspect of a model is prerequisite to the application to it of mathematical derivations. We hold metaphors, as conceptual phenomena, to be partly holistic analogues (juxtapositions) where some similarities between two subjects (those which suggested the juxtaposition, the initial ground of transfer) may advance into the foreground as "discrete segments", but they are accompanied by less specified "chunks", or "mental images", given en masse. Such metaphors constrain and direct the reflection about the recipient subject; their success in scientific theorising, however, depends eventually upon their susceptibility to being taken apart and converted into models. A novel metaphor which gives rise to a model is an initial insight of similarity between two wholes, which however gives way to an explicit analogy in terms of specified components and their relationships at a further stage. The generation of models in science starts at the stage of metaphor at which there is certain rough insight of similarity processed later into a clearly delineated network of correspondences. This is the reason why the discussion of metaphor in science is not separable from the discussion of models and analogies. Hesse's notion of scientific model describes it as consisting of a positive analogy (a list of known similarities), negative analogy (a list of known dissimilarities), and neutral analogy. In our view of metaphor as a (partly) holistic mental representation of experience, and of its discretising as the means of generating models, the field of neutral analogy remains holistic - it is what remains in a model of the initial metaphor. The process of exploring a model in order to see how far it can be pushed (how much of the structure of the donor subject can be productively attributed to the recipient subject) can be (metaphorically) described in Ortony's terms as a digital conversion of the analogue field of neutral analogy into the discretised fields of positive or negative analogy. A further point which we want to make concerning the difference between model and metaphor on the basis of the above considerations is that the metaphor conceived that way as a general idea of juxtaposition of two domains - is a broader structure than a model derived from it and may serve more than one purpose. It can find multiple applications on different levels of scientific discourse through offering the possibility of focusing on different aspects of the donor and recipient subjects, that is, of transferring concepts between their different parts. The most obvious example of such a double function played by an extended metaphor on two various levels of the discourse of physics is the clock as a metaphor for the world. On the one hand, focusing on the mechanical aspect of its functioning (a mechanism as a sum of its parts; push and pull and matter in motion as the physical principles of operation) led to the mechanical world model. On the other, focusing on a very different aspect of the clock, the impenetrability of its internal mechanism accompanied by the visual accessibility of the indications on its face, seems to have directed Descartes' and others' thoughts when formulating or reconsidering the hypotheticodeductive view of science.

45

3.1.1.5. Preliminary specification of conceptual metaphors of functions other than modeltheoretical As we pointed out at the very beginning, metaphor is a heterogeneous phenomenon and any mode of investigation into this phenomenon going into more detail than just a minimal definition necessarily suits only some of its diverse manifestations. There are numerous sorts of metaphor playing a constitutive role in science which do not apply to the pattern presented above. The kind of metaphors which become invented and developed into theoretical models are not the only kind relevant to the enterprise of physical research. One aspect unnoticed whenever the occurence of metaphor in science is identified with the use of models is the metaphorical nature of common language, which provides the basis for this part of scientific description which is formulated in natural language. Any scientific description in words utilises the stock of underlying, or "hidden", metaphors pre-shaping our thought and language in its non-scientific application. Sometimes, these metaphors infuse scientific theories or explanations with hidden assumptions they carry with them, leading to wrong ideas. In any event, they provide a basis for making it possible to talk about the world, and so they constitute a soft bridge between pre-scientific and scientific conceptualisations of experience. Of such nature are, in particular, • ontological metaphors which allow us to refer to and reason about our experiences in terms of objects, and form the very base of thought and language including scientific theorising and scientific language. Metaphors like "causes=substances", "processes=objects", are ofthat kind; • spatial metaphors like "more=higher", "states=containers"; providing the language with which to speak of physical relations and changes. They cannot be subsumed under the category of scientific models and analogies but nevertheless perform the same function as underlying sources for the generation of linguistic expressions both in everyday and in scientific language, which has been described by Martin and Harre (1982) as the role of analogical models. They are to be analysed as conceptual metaphors secondarily expressed in language; • animisms, personifications, hylopsychisms; • synesthesis. Another aspect of metaphorisation marginalised by the discussion of metaphors focusing upon their affinities with models is their meta-theoretical function. Certain metaphors contribute to physics not by suggesting explanations for particular physical phenomena, such as the electric current or interference of light, but rather by embodying the underlying assumptions about the nature of reality and the possibility of understanding it. They do not undergo an evolution into models, but remain holistic at the cost of being imprecise and at the same time highly suggestive; such are absolute metaphors like secrets of nature and scientific discovery. These metaphors of the physical meta-theory structure the approach to the object of the physical study, the assumptions about the nature and knowability of the physical world, and about the relation between the object and the subject of experience in the search for scientific truth; in short, they inform the direction of the development of science and its self-understanding.

46

Further conceptual phenomena not identical to typical analogical models which come under our concept of metaphor are "metaphorical world theories",73 like the machine metaphor of the mechanist world picture. Unlike typical analogical models explaining phenomena in a particular area, they have unlimited recipient domain. One metaphorical world theory may appear in various more specified instantiations (and, consequently, give rise to different world models), as shown by the example of the clock and the working machine as two instantiations of the machine as the donor subject for the world. We have explained before why the machine metaphor is not to be regarded only as a pre-stage of a theoretical model; a metaphorical world theory may be displayed not only on the modeltheoretical but also on the meta-theoretical level of science. Only loosely related to theoretical models are exegetic metaphors, which reformulate by means of common concepts the contents of complex theories for educational purposes, as used in popular literature or instruction at school level. Some of them have achieved popularity and given birth to lexicalised descriptive expressions, which we call imagistic paraphrases. They name the quasi-narrative reformulations of the physical laws and processes which have become well-entrenched exegetical elements in renderings of physical theories, such as Laplace's superman, Maxwell's demon, time arrow, or heat death. They are scientific "figures of speech" in that their theoretical contents are fully paraphrasable in more abstract language; what gets lost in such a translation is the imagistic and emotive element, as in the case of literary metaphors. Although they are neither indispensable nor the primary means of conceptualisation, the imagery and associations which they bring with them may pertain to some extent to theory-making, occasionally becoming helpful to the reasoning of scientists. They also facilitate the appropriation of physical ideas by other fields of human creativity. 3.1.2. Metaphor and false hypothesis In what follows we will argue that it is improper to claim, as is frequently done in the literature on the subject, that a literal description of a given subject turned out to be metaphorical if what happened is that it turned out to be false, in the sense that it ascribed to a subject physical properties which it does not actually possess. Contrary to this, we claim that a literal description of a subject may turn into a metaphor if it is retained after it became clear that it was originally based on false assumptions. This will allow us to identify a class of verbal expressions which we call assimilative borrowings, linguistically and conceptually rooted in out-dated scientific hypotheses. The concept of metaphor has itself undergone a process of meaning generalisation that caused its partial merger with such notions as model, spatial image, analogy, and, particularly, with false hypothesis based on a supposed analogy with known processes. E.g. Muscari (1988: 429^430) speaks of "mistaking the metaphor for reality" and the history of science being "full of false idols, like 'ether', whose glitter and charm have enticed the bemused into believing that such figures really exist". For Rothbart (1984), Newton's hypothesis that light consists of vibrations similar to the vibrations of corpuscles in the surrounding air perceived as sound74 is a metaphor involving a projection from a donor 75

74

The notions "world theory" and "root metaphor", originated by Pepper (1942), are outlined in chapter 5. Cf. Newton 1717, 1952. Query 13.

47 semantic field belonging to acoustics upon a recipient semantic field belonging to optics, the semantic constant "a trembling motion in a medium". The literature on metaphor in physical science is full of references conflating metaphor with analogical hypotheses which, at some point in their history, turned out to overstate the analogies between the known processes and those for which the explication had been sought. We think that the failure to differentiate the false hypothesis and metaphor implies falling back upon the theory of science and language that is so deeply entrenched as to remain unnoticed, and which nonetheless supplies the patterns of thought structuring our view of the difference between past and present. This theory is that we are in possession of the means of knowing the categories in the world, in contrast with the past epochs. It consists in seeing ourselves as historically privileged in being able to judge the difference between mere metaphors and things-as-they-are. This theory associates metaphor with missing knowledge of facts and its substitution by analogy, rather than with linguistic and conceptual change. In such a view, the pursuit of knowledge is uncovering metaphors which were taken for literal truths. As more and more facts come within our apprehension, our category divisions are constantly moving towards a closer match with the natural joints of reality. The discovery of the falsity of the assumptions of the earlier stages of science is interpreted as showing that what one used to think of as literal was merely metaphorical; this amounts to debasing metaphor as a vehicle of error rather than of linguistic and conceptual shift. To call a false factual assumption a metaphor is to identify implicitly the knowledge of facts with literal language. Our position in this work will be the opposite ofthat taken by Black (1962: 228) who argues: There is certainly a vast difference between treating the aether as a mere heuristic convenience ... and treating it as 'real matter' having definite ... properties independent of our imagination. The difference is between thinking of the electrical field as if it were filled with a material medium, and thinking of it as being such a medium. One approach uses a detached comparison reminiscent of simile and argument from analogy; the other requires an identification typical of metaphor.

In opposing this view, we accept the difference pointed out by Turbayne (1970: 3-4) between "sort-crossing" and "sort-trespassing": While the former is to represent the facts of one sort as if they belong to another, the latter is to claim that they actually belong.

The difference between "sort-crossing" and "sort-trespassing"75 amounts to the distinction between metaphoric and literal similarity comparison. 3.1.2.1. Sort crossing and sort-trespassing For Turbayne (1970), sort-crossing consists of using a metaphor, while sort-trespassing consists of taking it literally. Referring to the presence of metaphor in physics, we will Metaphor can be described as a case of sort-crossing only with the reservation that the metaphor of sort-crossing seems to imply that sorts, or categories, are containers with clear-cut boundaries. We assume instead that categories usually have no clear-cut boundaries and the inclusion in a category is a matter of degree, but that we are justified in speaking about a difference of sorts whenever some central properties of the typical referents of a notion are missing in the new referent, i.e., when some well-entrenched semantic restrictions governing its use do not apply.

48 assume that it is more correct to speak of a metaphor whenever significant differences between the donor and the recipient subjects are largely acknowledged, and of a false hypothesis while speaking of an overstatement of similarity between two domains. In doing that, we follow Turbayne's recognition that "a metaphor is always a metaphor to somebody". Turbayne (1970: 14) claims that awareness of "sort-crossing" is a necessary condition of a metaphor: When Descartes says that the world is a machine or when I say with Seneca that man is a wolf, and neither of us intends our assertions to be taken literally but only metaphorically, both of us are aware ... that we are sort-crossing ... I say ' are aware'; but, of course, we must be, otherwise there can be no metaphor. MacCormac (1985: 37) shares our belief that the consciousness of as-if is necessary for a concept to be metaphorical, as indicated by his comment that Although not all metaphors are personifications, it certainly seems that all personifications are metaphors. One might object that primitive peoples who believe that rocks and trees are inhabited literally by animistic spirits presume personifications that are not metaphorical. In applying human attributes to these non-human objects, primitive peoples do not think that they are crossing categories. Davie (1963: 52) seems to be close to accepting the view that the literalness of an expression should be judged according to criteria depending on the frame of knowledge in a given era when he says: John Locke ... speaks of 'the animal spirits' quite unmetaphorically. Our emancipation from this world of thought is signalised in the distinction we make between 'spirituous' (used of spirits like alcohol, which are material) and 'spiritual' (used of spirits which are immaterial)... Our distinction between 'spirituous' and 'spiritual' was unthinkable for the eighteenth century ... We find we need some word to distinguish between those spirits which are methylated and those which are angelic. For Mandeville and his contemporaries no such distinction existed, nor it is clear that they felt the need for it. Davie points to Elizabethan physiology as the frame which neutralised the psychological and the material meaning of the word "spirit" or, rather, it would be more proper to say that it offered no ground for the differentiation of meaning into psychological and material.76 He concludes quoting from Berkeley that when we learn (§ 92) that 'the animal salts of a sound body are of a neutral, bland, and benign nature', it would be wrong to say that the physical properties of the salts are defined by analogy from the moral properties of a virtuous human character. 'Bland' and 'benign' are suspended between the physical order and the moral, partaking equally of both, and implying that the two orders are not ultimately to be distinguished.77

ibid.: 47. Davie's contention finds support, among others, in these passages from Newton in which the latter speculates about the "electric spirit" which is responsible for electrical phenomena that it "may be the medium of sense of animal motion and by consequence of uniting the thinking soul and unthinking body". Quoted in Home 1992: 199. Newton used the phrases "subtill matter" and "aetheral Spirit" interchangeably and wrote also that "Vapours and exhalations on account of their rarity lose almost all perceptible resistance, and in the common acceptance often lose even the name of bodies and are called spirits. And yet they can be called bodies in so far as they are the effluvia of bodies and have a resistance proportional to density." Quoted in McGuire 1966: 219. ibid.: 53.

49 An enlightening comment upon the distinction between metaphorical meaning on the one hand, literal categorisation along lines different from ours on the other, has been offered by Fleck (1936, 1983: 99-100), who quotes Andrzej from Kobylin examining, in the sixteenth century, the concepts of warm and cold, mixing up what we hold today to be altogether different domains. Emotional and intellectual states and aptitudes (courage, anger, acute wit) are manifestations of heat, which, at the same time, behaves both like a chemical property and a physical state, in the contemporary senses of these notions. Contrary to the first impression, these are not to be regarded as metaphorical applications of the word "warmth": ... wir lesen, daß die Kälte des Alters die Fingernägel und das Haar bleicht, 'weil alle Kälte bleicht, wie die Hitze sengend rottet', oder daß der Wein den Alten natürliche Wärme verleiht, die in ihnen schon nachläßt. Oder daß die Glut des Hungers rohe Speisen garen und sie verdaulich machen kann. Diese Glut, diese Wärme, ist also in all ihren Formen identisch, weil sie sich austauschbar ersetzen können: ihr Wesen bleibt gleich ... Wir haben somit ein vollendetes Anschauungssystem: ein und dasselbe ist die Wärme des Feuers, die Hitze des Temperaments oder Affekts, die 'heiße' Würze der Speisen, das Brennen des Hungers, die Wärme des Federbetts und junger Kinder usw. ... Es gibt keine Differenzierung dieser fünf für uns verschieden Arten der Wärme ... Implizit ist darin die Anschauung enthalten, daß "Feuer" und "Leben" irgendwie gekoppelt sind, keineswegs bloß in übertragener oder symbolischer Art: sie sind irgendwie in ihrem Wesen identisch ... Es bestand ... ein unklarer, aber zu einem System ausgebauter Gedanke einer grundsätzlicher Identität von 'Feuer' und 'Leben'. Es bestand ein auf ihm gestütztes Begriffspaar 'kalt-warm', das jenen Gedanken der Verbindung des Feuers und des Lebens enthält. Diese Begriffe haben sich umgestaltet: sie haben sich differenziert und sozusagen in mehrere Bedeutungen geteilt. Eine gewisse Bedeutung hat den Wert einer 'physikalischen Bedeutung' angenommen, ein anderer den Wert einer 'übertragener Bedeutung', einer uneigentlichen, poetischen ... Bedeutung. Der spezielle Denkstil ... der modernen Physik ... hat die 'Kälte' verworfen und der Wärme einen ganz anderen Inhalt als den gegeben, den sie früher hatte ... Gehen wir heute mit unserem wissenschaftlichen Denkstil an die Lektüre alter wissenschaftlicher Schriften heran, unterstellen wir den Worten unwillkürlich die heutigen Inhalte. Unter 'Wärme' möchten wir die heutige 'physikalische Wärme' verstehen, oder auch die heutige 'Wärme in poetischer, übertragener Bedeutung'. Aber dieses Wort bedeutete sowohl das eine wie das andere zugleich, denn eine solche Differenzierung hat es damals noch nicht gegeben. Deshalb läßt es sich überhaupt nicht genau in die heutige Sprache übersetzen, (italics in original)

At another point, Fleck quotes Odilo Schreger's elucidation of "heaviness" in "Studiosus jovialis" (1755), to argue that Der Begriff der Schwere, mit dem wir es hier zu tun haben, unterscheidet sich völlig vom heutigen physikalischen: Er enthält einen undifferenzierten Komplex von Inhalten der heutigen Begriffe der Schwere, der Schwerfälligkeit, des Schwermuts und der Schwierigkeit (Unhandlichkeit) beim Heben ... Gegen einen solchen Schwerebegriff kann man nichts einwenden, weder vom logischen noch vom empirischen Standpunkt aus. Die Waage ist keineswegs ein Instrument, diese Schwere zu messen ..."

What we said above amounts to the claim that a literal meaning may become metaphorical if a previously unknown or disregarded difference between the primary and secondary domains of reference of a word is acknowledged or turns out to be essential owing to new insights. This claim means that we do not fully agree with the well-known account of the "life story" of metaphor summarised briefly in a well-known aphorism: "yesterday's metaphors are today's truths". Turbayne (1970: 24-25) elaborates on the latter subject saying that 71

ibid.: 106.

50 There are three main stages in the life of a metaphor. At first a word's use is simply inappropriate. This is because it gives the thing a name that belongs to something else. It is a case of misusing words, or 'going against ordinary language', and, therefore, of breaking conventions. Our first response is to deny the metaphor and affirm the literal truth ... But because such affirmation and denial produce the required duality of meaning, the effective metaphor quickly enters the second stage in its life; the once inappropriate name becomes a metaphor used by us with the awareness to illuminate obscure or previously hidden facts ... The moments of inappropriateness and triumph are short compared to the infinitely long period when the metaphor is accepted as commonplace. The last two stages are sometimes described as the transition from a 'live' metaphor to one 'moribund' or 'dead'. But it is better to say that either the metaphor is now hidden or it ceases to be. (emphasis HP)

Turbayne assumes, then, that metaphorical expressions go from the "live" stage of development: a deviant, non-orthodox application, to the "dead" stage when the new meaning receives equal footing with the original one. In other words, a metaphor starts with a conscious misapplication of a word (sort-crossing), followed by the process of generalisation of meaning through an assimilation of a concept to the new domain of application. This account, we argue, is well applied to the process of metaphorical stipulation of meaning, but there are metaphors which start their lives as literal names. Sometimes there is a phase in the "life story" of a metaphor prior to that which happens in Turbayne's account. Such a metaphor starts with the literal application of a concept. Sometimes, a literal application of a concept (to a new set of referents) is based on mistaken premises (sorttrespassing - overstated analogy or similarity),79 and the metaphorical stage does not begin until the erroneous character of the premises becomes disclosed as a result of further research. If "a metaphor is always a metaphor for somebody", then a "metaphor" not recognisable as such is a literal truth. A metaphor arises if, after the discovery of an essential difference between one sub-class of referents and the rest, an associated notion or set of notions is not abandoned altogether but gradually becomes generalised (its core meaning undergoes reduction or restructuring) to suit equally well both domains of reference, or receives a second meaning different from the first (in the case of nouns, typically supported by an adjectival or nominal modification). It is only after the assumed relation between the two domains of reference - that of a superordinate and a sub-category - turned out to be misleading that the metaphorical process, the meaning change, begins. This process of change may be of two kinds: • the category to which the word refers changes its scope because the shared features of the secondary and the primary subject are made more salient and become the central meaning components of a category, which thus becomes redefined to include the instances of the recipient subject on equal footing with the instances of the donor subject (the wave notion applied to water waves and light); • a new, distinct meaning (category) emerges under the retention of old wording (the electric current). We define metaphorical speech as that in which a word or expression is used in a sense which is deviant, or non-orthodox, that is, which differs significantly from the usual meaning through excluding some of its central components. This definition of the literal and the Rendering this process in traditional linguistic terms, we would speak of the growth of extension (= scope of reference) without the change of intension of a word or phrase.

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metaphorical disagrees with the trend to apply the notion of metaphor to cases of tresspassing such as the hypothesis of corporeal ether, or the "electric fluid" before the elimination of the fluid theory of electricity. The latter is done frequently in the literature on the scientific applications of metaphor. We argue that this assumption fails to differentiate between the process of meaning transfer and non-intentional "category mistakes" - false categorisations: of light as the oscillation of parts of a material medium analogical to air as the carrier of light, and of electricity as the transport of a material fluid substance. The fluid theory of electricity and the history of the wave concept exemplify the metaphoric process which went through a stage of development counter to the typical direction from metaphorical to literal. An overstated analogy plays the same role in the vocabulary of physics as the underlying metaphor: they both "spin off" a matrix of terminology for a given domain of experience. However, the expressions generated from an underlying metaphor can be classified as metaphorical on reflection through the comparison of the semantic field of the donor subject with the domain of the recipient subject. Contrary to this, the expressions derived from a false hypothesis do not only appear, but actually become metaphorical only as a result of a new discovery. We refer to this process using the term "assimilative metaphor". Our first example of assimilative metaphor is the change of the semantic restrictions on the use of the word "fluid" following Lavoisier's discovery of the conservation of mass. This discovery led to a new semantic restriction on the application of the concept of a substance and, as a result, such a meaning change of the notion of a fluid that after some time the previously literal notion of the electric fluid and its "current" could only be used metaphorically. The second example comes from the history of the wave concept. Light was initially thought to be constituted by displacements of particles of a material medium called ether. However, no attempts to describe the physical properties of a substance which could carry all the observed properties of light succeeded, and the introduction by Maxwell and Hertz of a mathematical description (interpreted in terms of changing distribution of energy) for which the mechanical properties of ether were of no relevance made the ether concept actually redundant. However, the concept of wave survived the death of ether, stripped from its initial mechanical component - the displacement of material particles of the medium. For an indefinite period of time, by which we mean the transitory period of meaning change (the change establishing itself in the physical theory and, correspondingly, on the level of lexical semantics), the wave concept was applied to electromagnetic phenomena metaphorically: it was recognised that the usual inferences from the known properties to further properties of the referent could not be drawn, so that the semantic network associated with the wave concept was disturbed. From the fact that electromagnetic waves show e.g. interference effects we cannot conclude that there are oscillating particles involved. Both the fluid theory of electricity and the wave concept as applied to electromagnetic phenomena may only be classified as metaphorical after it has been recognised that the similarities previously assumed to hold have been overstated. We argue that at the time of their introduction they were seen as literal descriptions of the subject matters and therefore the name of metaphor does not apply to them at that stage.

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3.1.2.2. A definition of literal similarity? Most attempts to define metaphor invoke the notions of similarity and difference: a metaphor is differentiated from a literal similarity comparison. Is it, for this purpuse, possible and necessary to define the notion of literal similarity itself? Opinions are divided. Knorr-Cetina (1984)80 regards similarity and difference ("Distanz") as primitive notions which cannot and do not need to be further analysed. We already indicated what we regard as a literal similarity comparison when we characterised a metaphorical expression as leaving out some central meaning components of the same expression used literally. Gentner (1982) gives an alternative formulation, also by means of comparative decomposition of meaning, of the difference between the literal versus metaphorical (analogical) juxtaposition of two domains of experience. Her analysis, for which she claims the merit of giving a satisfactory definition of literal similarity, depends wholly on the assumption that it is the one-place attributes that determine the degree of physical similarity between the objects compared. In what follows we will pursue her proposal in more detail, which will lead us back to the problem of the "difference of sorts" and the process of changes in categorisations, as well as in the criteria for categorising things. Gentner defines metaphor as denoting such mappings between subject domains as apply the same relations to dissimilar objects, that is, objects showing different attributes. She makes a strong distinction between objects and their attributes on the one hand, and relationships on the other. In a metaphorical (analogical) juxtaposition, the mapping of structures between the donor (base) and the recipient (target) domain is such that many of the relational predicates valid in B must also be valid in T, while, at the same time, relatively few of the valid attributes (the one-place predicates) within B apply validly in T.81

She describes the difference between comparison statements conveying literal similarity and analogical (metaphorical) relatedness as determined by the degree of matching among the one-place attributes of the component objects and the degree of matching between their relational structures: When both the component object attributes and the relational structure overlap, the comparison is one of literal similarity.82 Her example is: The helium atom is like the neon atom.

"Das Analogie-Räsonieren basiert auf einer Ähnlichkeitslogik, in der der Begriff der Ähnlichkeit sowohl ein primitiver als auch ein logisch grundlegender ist: primitiv in dem Sinne, daß er nicht mehr weiter reduziert oder erklärt werden kann, und grundlegend in dem Sinne, daß er vom Beginn des Spracherwerbs her vorausgesetzt werden muß. Es scheint, daß man metaphorische Klassifikationen von anderen Arten des Analogie-Räsonierens am besten durch das Ausmaß der Distanz unterscheidet, die zwischen den beiden durch die Ähnlichkeitsklassifikation zusammengebrachten Systemen besteht." (Italics in original.) Knorr-Cetina 1984: 94-95. Gentner 1982: 109. ibid.: 110.

53 This is a literal similarity comparison, because there is considerable overlap both in the component objects - protons, neutrons, and electrons - and in the relations between those objects.83

Metaphorical relatedness, on the other hand, is characterised by a relatively low degree of match between the attributes of the physical objects involved (one-place predicates) and a relatively high degree of match in relations (two- or three-place predicates). This approach could easily be applied to the early ether wave theory and the fluid theory of electricity which we will treat in the next section, and it would indeed be very favourable to have a set of criteria to hand which would make us capable of an objective measurement of literalness of a comparison. However, the general objections it raises prevent its application. One deficiency in Centner's approach is that speaking of a match in one-place attributes, she seems to mean throughout the similarity of measurable magnitudes (amounts) of these attributes, e.g. similarity of size, rather than of the objects being similar in being characterised by these attributes. It seems reasonable, though, to include the latter in the sense of literal similarity. Ether was a substance physically similar to air in view of their both being characterised by a certain density and elasticity. For Euler, ether is 1000 times less dense and more elastic than air; nevertheless, it is rather obvious that in view of their both manifesting these properties, they are to be thought of as literally similar and not analogically related. Further, the difference between properties and relations is not always a clear-cut one: for example, the property of fluids known to eighteenth century physics as their "elasticity" can also be conceived in terms of its hypothetical underlying cause and expressed in terms of the relation between the component particles, namely, their mutual repulsion. A simple "attribute" like weight can be reformulated in relational terms, as the result of gravity, mutual attraction of two bodies. Moreover, it seems that some physical characteristics which we would tend to qualify as the basis of a literal similarity comparison are not always apprehended and formulated as one-place predicates. "Ionised" (= "containing ions"), or "consisting of compound molecules" are relations (between a whole and its component parts) rather than attributes, and seem to constitute nevertheless literal similarities between two substances. One could argue that, for example, in the latter case the similarity is literal because the elements of the systems compared are literally similar in being compound molecules. But it is the systems (substances) which are compared here, and not their component parts, and so the desired result (literal similarity) could only be obtained through a shift of topic from the whole to its part, which is a major step in conceptually reconstructing the whole act of comparison. Moreover, compound molecules differ greatly from one another (consider the complexity of structure of organic substances), and in order to obtain the "literal" (in Centner's terms) similarity of the component objects we would have to descend to the level of atoms and to draw conclusions in turn about the similarity of atoms from the similarity of their component parts (protons, neutrons, etc.). Of course, the comparison on that level produces considerable literal similarity for each pair of physical objects. This applies to any kind of similarity judgement, including those cases where the things compared are available to direct sensual perception. It is even hardly possible to give a definite verdict on whether an act of comparison between a referent and the prototype of a 85

ibid.

54 tiger (or, classically speaking, the meaning of "tiger"), leading to a categorisation judgement such as "This animal is (not) a tiger", contains a relatively high number of one-place attributes compared to relational properties. Attributes or relations, it is the degree of participation in the set of properties determining the usual application of the word "tiger" which makes them relevant for the act of comparison (between a concept and an instance) and makes it more or less literal. We suppose that the question of what constitutes a literal similarity between physical objects cannot be fully satisfactorily answered in terms of the distinction of one-place and more-place predicates only, being related to the question of what makes physical sorts. As far as Gentner's position is concerned, she is right in so far as the aspects of the physical world perceived and conceived of as properties of objects (and expressed as one-place predicates) have always strongly participated in defining physical categories. Generally, however, the answer to the question of what defines a category may depend on a number of different considerations depending on the tastes of one or other scientific period applying different criteria in making such judgements. Ponderability was an attribute irrelevant to the membership in the physical sort "fluid substance" before Lavoisier's discoveries, but turned into its criterion afterwards. If we accept Gentner's criteria, then e.g. various sort of waves mechanical, electromagnetic, "waves of probability" of the quantum theory - are analogically related rather than literally similar. But numerous authors would insist today that they are literally similar because they share the central aspects of physical description in contemporary theoretical (mathematical) terms, which is essential for the meaning of the notion "wave" today, although different from those of the middle of the nineteenth century. One can claim that he contemporary concept of wave applies equally literally to various sorts of waves, although it is itself of metaphorical origin (because created by metaphorical extension of the original meaning). Given the conceptual, theoretical, mathematical devices worked out in the meantime, such as Maxwell's equations, the concepts of energy distribution and indeterminacy of physical processes etc., we are at the same time given different criteria to judge similarity of physical phenomena. What we propose, then, is that our definition of metaphorical versus literal comparisons in science should not be based on our era's own criteria of similarity judgements; instead, we should give consideration to the criteria internal to each era when making such judgements. Already our definition of metaphor as an "as-if" construct including the conscious deviance from the conceptual and linguistic norm implied that it is not ours but the epoch's norms which are to be regarded as the point of reference. In the next section we want to briefly consider some consequences of the latter view and see whether it can be consistently maintained. 3.1.2.3. Today's metaphors: yesterday's literal truths? We have stated that similarity judgements do not depend on a constant set of criteria but change together with the whole frame of available knowledge, and that the criteria relevant for similarity judgements are partly the same as those which participate in the judgement of membership in what we called physical sorts. Generally, a similarity between physical objects which makes them belong to one category in one period may be disclosed as similarity of properties of secondary importance for the formation of categories in another period.

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We are to choose from two options concerning the stand one may take towards this recognition: - to allow the distinction literal/metaphorical depending on the criteria defining categories internal to each scientific period rather than a consideration in terms of some fixed set of criteria; - to judge concepts, theories, expressions etc. as metaphorical on the basis of their violating the boundaries between our own present-day categories. That would mean agreeing that they might have been thought of as literal (based on literal similarity) at some time, but to regard them as being "in fact" metaphorical because they sort-cross categories which we regard as adequate descriptions of reality. We decided to object to the latter option, which excludes the consciousness of "as if" from the notion of metaphor and, thus, obliterates the difference we insist upon between sorttrespassing and sort-crossing. In other words, it obliterates the difference between a counterfactual hypothesis on the one hand and metaphor on the other. However, there is also an immediate problem with allowing the difference between metaphorical and literal to depend on the criteria for categorisation peculiar to each era. It might seem to necessitate the conclusion that the prevailing majority of extended metaphors in physics were literal descriptions of physical reality at some stages of their existence. Take, for example, the machine metaphor which seems to have had for some time such an immense impact that it made man and the machine conceptually members of the same physical category - working objects. This category, containing at the central position the component(s) "capable of performing useful action through moving weighty objects against an opposing force", provided for the emergence of the concept of "mechanical work" and underlay Mayer's physiological considerations following from his contention that "Die Leistung eines Mannes, der mit großer Anstrengung ein Gewicht frei hält, ist = Null" (see section 4. 2. 2.) This would mean that at least some researchers took the "working machine" metaphor literally at the period closely following the industrial revolution: the similarity consisting in the ability to perform useful work through moving physical objects was taken to be more relevant to the formation of a physical category than the dissimilar features. The category of working objects was thought of as being more relevant to the physical description of the world - more physically real - then the categories "human being" and "inanimate object". If this view is right, one might argue, then this and all other long-lived (nontemporary) metaphors of science went through a period in which they constituted literal similarity statements just because they afforded the formation of new categories which were assumed to correspond to important lines of division in the physical world. However, in this case to talk of them as metaphorical only makes sense if we again fall back upon our present-day criteria. We may then speak of them as being taken literally in their own time and metaphorical "in fact", and the distinction between a counterfactual hypothesis and sortcrossing categories becomes neutralised again. The way out of this inconsistency is to point out that the usual categories "human" and "machine" based on the usual set of criteria (meaning components, semantic restrictions) were conceptually available even when paralleled by the "working object" concept. A metaphor divides the world into categories using criteria for category formation which are new and different from the usual, but it does not relegate the usual categories out of existence. A false hypothesis, on the other hand, uses the standard set of categories and

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criteria for their formation but puts into them things which do not belong there on the assumption that they fulfill the criteria. We think that the distinction should be maintained and that a proposition should be judged as a metaphor rather than a literal consequence of a false hypothesis if, in its own time, - certain differences between the donor subject and the recipient subject were acknowledged, - concepts and categories were available in view of which these acknowledged differences were essential for membership in a category. It remains to be said that the degree in which a metaphor (from the present-day point of view) may be judged to have constituted a piece of literal truth in its own time depends on the degree in which the sum of knowledge of this time, including the humanities and common sense as well as exact sciences, offered different perspectives, or different conceptualisations, of the same recipient subject, allowing the alternative conceptualisations to appear as illuminating metaphors rather than literal truths. Obviously enough, the comparison made between humans and other kinds of beings has always been paralleled by the consciousness that they are members of distinct categories because, whereas comparisons between physical systems lie mainly within the domain of the exact sciences which have decisive power in the formulation of concepts to deal with them, concepts concerning human beings are available independently from physical theory. The differences between machines and humans hardly lend themselves to such a degree of marginalising as to allow the relation between them appear as that of literal similarity. The extent to which the authority of physics took the upper hand in the period when physics took it upon itself to include human (and animal) beings in its discourse domain determined the extent to which its mechanical metaphor was taken literally, but the counter perspectives have always been at hand, blocking any serious shifts of category structure. 3.2. A working definition of metaphor • "Metaphor" denotes a range of phenomena ranging from the primarily linguistic to the primarily conceptual which can be expressed in linguistic form. It pertains to the levels of (1) cognition, (2) lexical semantics, including word-formation, (3) surface language. The functions of metaphor corresponding to these levels are, respectively, (1) structuring experience, (2) affecting semantic changes, (3) verbal expression. • Metaphor consists of the transgression of conceptual and/or linguistic incompatibility of two notions/domains of experience through a restructuring within their conceptual and/or linguistic representations. It is characterised by the occurrence of the donor subject and the recipient subject. The donor subject provides the conceptual structure and/or the verbal expression for the recipient subject which is typically a lesser known domain of experience.84 We choose to neglect the possible differentiation between epiphor and diaphor. We marginalise the diaphor defining metaphor as epiphor, which we take to be the prevailing and representative mode of metaphor in physics. In a diaphor, there is no clearly delineated donor subject, neither on the level of the surface language nor on the level of conceptual structure. It consists of bringing together two

57 • The concept of "as if" is central to the notion of metaphor: the scope of significant dissimilarities between the donor subject (conventional reference of a concept or expression) and the new instance (the recipient subject) must be realised or potentially available to reflection without recourse to hitherto unknown differences between both domains. The "as if" concept defines the difference between sort crossing and sort trespassing - the conscious application of language and concepts peculiar to one domain in another domain recognised as essentially different, and their misapplication on the basis of misconceptions concerning the degree of similarity between the primary and secondary subject. • It is not possible to draw a clear-cut boundary between metaphor as a linguistic phenomenon and metaphor as a way of viewing reality - a redescription or reclassification of experience. Each novel conceptualisation of experience finds its reflection in language. However, in our view, metaphors differ in view of the participation of the conceptual factor in the transfer of expressions. That is, they differ with respect to how far the function they perform is primarily linguistic or primarily conceptual. The corresponding spectrum of demands fulfilled by applying a metaphor stretches from filling evident small-scale gaps in vocabulary (providing denotations for single concepts) to providing rules of conceptual manipulation for larger domains of experience. • Both the donors and the recipients of metaphors differ widely among themselves as far as their scope is concerned. The scope of the recipient subject/domain may be as narrow as a new physical device for which a name is sought, or as broad as the whole of the physical world. The metaphorical process may be constituted either by a direct juxtaposition of the donor and recipient subjects of a given expression (isolated metaphor), or by a conceptual juxtaposition and transfer of structure between broader domains of experience structured in networks of concepts (extended metaphor).85 In the latter case, it may be expressed on semantically incompatible notions. Diaphors may be, for example, "process metaphors" which release selectional restrictions on the (dis)congruity between a subject (noun) and a verb. We explain the existence of diaphors and epiphors by the fact that a violation of a strong semantic restriction on the applicability of a given notion typically corresponds to re-categorisation of its recipient subject, which is an epiphor, but not in all cases; if not, a diaphor is produced. We think that an expression where the donor subject is absent on the level of the surface language should be viewed as a diaphor either if it cannot be traced back to a corresponding underlying epiphor, or if such a translation, even if possible in principle, would produce no cognitive gain. Whether a metaphorical expression is to be classified as a diaphor or as a satellite verbal expression of an underlying epiphor is a matter of how much is gained in such a conversion for our understanding of the semantics of the metaphor and the underlying cognitive process. The predicate "work" applied to a machine, where there is no donor subject expressed on the surface, is a verbal expression of an underlying epiphor detectable on reflection (man=machine) and reveals the influence of the industrial revolution on the perception of human beings and their activity. The terms "diaphor" and "epiphor" are used in a rather diversified way, referring to binary classifications of metaphors on somewhat disparate lines by diverse authors, see e.g. Wheelwright 1962, MacCormac 1985. Diaphor plays a marginal role in our subject, the reason being that we have almost always succeeded in tracing linguistic diaphors back to conceptual epiphors, that is, in finding a donor subject/domain implied by a given expression even if not present on the level of surface language. The binary differentiation between isolated metaphor and extended metaphor is applied e.g. by Kittay 1987. Her notion of isolated metaphor largely overlaps with our notion of linguistic metaphor. We do not identify isolated metaphor and linguistic metaphor because we regard as a significant group and devote much attention to linguistic metaphors which are not isolated but derived from extended metaphors.

58 the linguistic level by the use of language violating and, on the long run, changing the semantic restrictions with respect to the whole semantic network of the donor domain. We subsume the interrelated levels of surface language (verbal expression) and of lexical semantics under the notion of the linguistic aspect of metaphor. Differentiating between metaphor as a linguistic device and metaphor as a conceptual structure, we will talk of linguistic metaphors on the one hand and extended metaphors on the other. We regard the passage from the literal to the metaphorical as a spectrum ranging from an application of a word/concept to new instances only slightly different from the up-to-now referents, through the similarity-based extensions of reference, to the transfer of denotations to a substantially different sort of instances on the grounds of remote similarities and the projection of meaning into entirely new domains. Metaphorical conceptualisation as well as verbal expression of a metaphor may be singular cognitive and linguistic events or they may, in certain circumstances, acquire stability in thought and language. A verbal expression of a metaphor which acquires stability affects changes on the lexico-semantic level of language.

3.3. Sorts and functions of metaphor in physical discourse 3.3.1. Classifications of metaphors in science The diversity of metaphor in its contribution to physical science allows applying diverse classifications as a frame for a systematic presentation of particular manifestations of metaphorical processes. Several options could be considered as criteria of such a systematic division: • Classification according to the donor domain. Examples: spatial metaphor; animations and anthropomorphisms. • Classification according to the recipient domain, that is, the particular branch of physics. Examples: optics; classical mechanics; wave mechanics; quantum theory. • Binary classification according to Boyd's (1979) criterion "theory-constitutive" vs. "expressive" or "educational" metaphor. • Binary classification in diaphor and epiphor following Wheelwright (1962) or McCormac (1985). • Binary classification in stipulative and evolutionary metaphors, following Rotbarth (1984). • Classification according to novelty vs. entrenchment in the conceptual and linguistic system existing prior to the generation of a given metaphor, correlated with the degree to which a given metaphor is peculiar to physics vs. rooted in the general language. • Binary classification in extended vs. isolated metaphors, according to the scope of the semantic domain affected by the transfer. • Binary classification in linguistic vs. conceptual, according to the criterion "transfer of designations" vs. "transfer and extension of concepts", correlating highly with the previous one (extended vs. isolated). • Classification according to the functional level, e.g.: denomination - formation of general and theoretical concepts - education - style - metatheory.

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Obviously, each of these possible classifications applied to the facts to be presented produces "sort-crossings" of groupings which would be formed by using other criteria. We have arranged our samples in such a way as to minimise the unavoidable sortcrossings. Our primary distinctions are those between different functional levels of metaphor in the physical discourse, and those between linguistic and extended metaphors. 3.3.2. Sorts 3.3.2.1. Extended metaphor • We shall use the notion "extended metaphor" to denote such metaphors which consist in conceptual juxtaposition of two broader domains, which may trigger metaphorical application in the recipient domain of a number of concepts and expressions referring primarily to the donor domain. In current linguistic practice, the expressions "extended metaphor" and "underlying metaphor" are used as synonyms.86 We define the underlying metaphor as a sub-class of the extended metaphor. • Extended metaphors are primarily conceptual phenomena and are only secondarily manifested in verbal expressions derived from them. They assimilate two distant domains of experience under a partially common conceptual structure and, in the cases in which they are actualised in language, a partially common semantic network. The semantic transfer does not consist of the direct transfer of denotations; rather, the extended metaphors serve as an underlying source of symbolic relations. That is to say, they are not to be located on the level of particular verbal expressions, like words or phrases. The symbolic relations between two domains of experience established by extended metaphors provide the basis for generating a potentially infinite number of verbal expressions from which only a certain number becomes lexicalised, others can be generated anew any time. An example of an extended underlying metaphor is "time=space of events", lifting the semantic restriction on the use of the primarily spatial prepositions and allowing them to be used with reference to time. The extended metaphor "man=machine" led to the establishment of the lexicalised satellite metaphor "mechanical work". • Extended metaphors can give rise to scientific models. Such scientific models are nonverbal manifestations of extended metaphors. They contribute to the verbal manifestations of the extended metaphors on which they are based functioning as sources of satellite linguistic metaphors. • Our notion of "extended metaphor" covers several different sorts of metaphor and extant theoretical notions: A. "Absolute metaphor", a notion based on Blumenberg (1960). By this, Blumenberg refers to pre-theoretical assumptions which, by their nature, resist any attempt at translation into the precise definition-based language of scientific terminology, but which constitute the premises of scientific research. They are exemplified by the notions of the secrets of nature and scientific discovery. It is not possible to recover fixed and clear meanings of such metaphors; what we can do is to recover their position in a discourse, a meaning which is complex and indeterminate. The function of "absolute" metaphor " is the one which we identified as "meta-theoretical" Cf, for example, Levin 1988.

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and characterised as structuring and articulating the approach to the object of knowledge in general and physical science in particular, the view of the aims and possibilities of scientific research, defining the kind of questions which can reasonably and meaningfully be asked and, in short, informing the self-understanding of scientific research. B. "World theory", a notion introduced by Pepper (1942). Metaphorical world theories are metaphors distinguished by unlimited scope of the recipient domain; their donor domains (="root metaphors") tend to be applied as the source of "basic concepts of explanation and description"87 for multiple aspects of reality and the whole of the physical world. The notion "world model" is sometimes used in a similar way. We differentiate between a world model and a world theory, referring with the former term to the concept-theoretical aspect of a world theory as differentiated from its pre-theoretical aspect, including epistemological assumptions relevant to scientific method. Exemplified by the metaphor "world=machine" (with its root metaphor "machine" applied as a principle of explanation to cosmos, state, and human organism), and by prescientific personification of the non-human world (man as a donor domain and a general explanatory principle for the world) manifest e.g. in hylopsychic explanations of gravitational phenomena. C. "Underlying metaphor" of Lakoff and Johnson (1980). A stock of basic culture-specific conceptualisations of more abstract domains in terms of domains more closely related to direct experience. Exemplified by the spatialisation of time and metaphors "more=up" and "states=containers" underlying the spatialised models of energy in quantum mechanics. D. The basic idea of comparative juxtaposition of two given domains which may become implemented and developed in an analogical model (of a smaller scope than a "world theory") making no claims to reality as describing actual mechanisms of nature; e.g. atom as a miniature solar system; also an out-dated scientific hypothesis assuming a generic identity of two kinds of processes or entities which had to be re-classified as generically different as a result of new discoveries in the donor domain or the recipient domain. We regard such hypotheses as extended metaphors insofar as they have given rise to the terminology which remains in use, and still direct the conceptualisations of the recipient subjects. 3.3.2.2. Linguistic metaphor • In defining metaphor in its linguistic aspect, we presuppose the following notion of meaning: - Meaning of a lexical item is the semantic hypothesis with respect to the proper use of this item, analysable in terms of semantic restrictions governing its use. It can also be Pepper 1942:91. Further, we also regard these formulations as compatible with the notion of the semantic network or field. It has been argued, e.g. by Kittay (1987), that conceiving meaning in terms of semantic components is incompatible with the conception of semantic field, but the controversy seems to be verbal: the two representations are incompatible if we understand rendering of meaning in terms of semantic components as a conjunction of semantic simplexes, context-independent "atoms" of meaning. Kittay allows for representing meaning in terms of semantic descriptors, which are concepts articulable in language although not necessarily in monolexemic terms, as compatible with the concept of semantic fields; they are "not the building blocks of meaning, but points of inter-

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alternatively formulated in terms of semantic components. We hold these formulations to be equivalent to each other.88 -The semantic restrictions are graded in their relevance. In the alternative way of speaking, it corresponds to the different degrees of entrenchment of particular components in the meaning of the expression. The semantic components include well-entrenched central components and a body of less well entrenched, or marginal, components (associated commonplaces). The central components are those which are most usually displayed by the referents of a word in current linguistic practice, and are therefore regarded as essential for the object to be seen as a "proper" referent of the word, and listed in dictionaries. - There is no clear-cut border line to be drawn between the "meaning" and the "commonplace knowledge" associated with a given word and concept. - Full componential analysis of meaning is impossible a priori, that is, out of context. The meaning of a word is not exhaustible by enumerating its components (semantic restrictions) out of context. This follows from our assumption that there is no clear-cut boundary between lexical and world knowledge, from the context-dependence of conceptualisation, and from the difference between the partly holistic mental representation of a concept and its semantic representation in terms of component features. The verbal expression of a metaphor consists in violating the semantic restrictions on the application of an expression so that an expression whose usual reference belongs to the donor domain becomes applied to the recipient subject. An expression is used metaphorically if the semantic restrictions on its use are violated to a large degree. That is, the metaphorical application of an expression is the one which excludes at least one of its most central components, highlighting some other, central or marginal component(s) of its meaning. The literal application of an expression is the one in which most relevant semantic restrictions are adhered to, that is, all or most central components of meaning of the category are perceived as present in the referent. The difference between the literal and the metaphorical meaning of an expression is a matter of degree and depends on the number and the relevance of the semantic restrictions which are violated when an expression becomes applied to the secondary subject.89 If the two domains to which an expression is applied are the direct sensual or sensomotoric experience on one hand and more abstract relationships on the other, the former typically constitutes the donor domain and the latter the recipient domain. Metaphorical expressions can be satellite metaphors of extended metaphors conceptually juxtaposing broader domains, or can be based on a novel act of a direct juxtaposition of the donor subject and the recipient subject of a given expression. The novelty of metaphor connection through semantic fields" (1987: 256). Her semantic descriptors are our semantic components. In what follows we will feel free to apply the notion of semantic network. In everyday language, the judgements of how different a new instance must be from the old instances for an expression to be no longer literal would be based in practice on frequencies of use or statistical generalisation of intuitive judgements of language users. In science, the issue is more complex. For example, MacCormac (1985) goes very far in classifying scientific applications of words and concepts to new instances as metaphorical. The use of "angular momentum" by Bohr in quantum physics is for him metaphorical because it expresses a continuous function in classical mechanics and a discontinuous, quantised, function in Bohr's atomic theory.

62 is a matter of degree because metaphorical expressions are rooted to different degrees in the established patterns of conceptual juxtaposition. The assumption that the verbal expression of a metaphor involves an application of a word which leaves out some of the central features of the donor subject is what we share with all the previously mentioned proposals suggesting a comparative meaning decomposition as the means of dealing with a metaphorical expression. However, such proposals are frequently implicitly based on the traditional "atomist" theory of meaning, implying the comparison theory of metaphor. The "atomist" approaches to meaning assume an inventory of elementary semantic features, sharply defined and enduring and relatively stably interconnected, as the basis of categorisation underlying matching of referents with lexical entries. In such a view, a metaphor appears to result from the need to express some features of the primary subject which it shares with the secondary subject. Thus, each metaphorical expression appears to be based on a similarity prior to the act of applying a notion metaphorically. In our approach, however, we want to differ from the comparison theory, maintaining that there are instances of metaphor that are meaning-making rather than meaning-expressing, that is to say, the similarities they invite us to consider are created, or projected, rather than just highlighted by comparison: "metaphor ... neither presupposes nor supplies a list of the respects in which the subjects juxtaposed ... are similar."90 The judgement of similarity between the primary and the secondary subject of a metaphorical expression depends on the conceptualisations of the donor and the recipient subjects of metaphor, which themselves do not remain unaffected by the act of their juxtaposition. Our proposal for amending this deficiency of the lexical similaritybased approach is to state that the meaning of a word is not fully exhausted by decomposition into semantic constituents out of context. Correspondingly, there are no contextless similarity judgements. Any property can become the basis of a positive similarity judgement, also such as is seldom topicalised or consciously perceived as characteristic of a given thing. An expression situates its referent(s) in a certain conceptual context. As this is the context which determines (organises) the conceptualisation associated with the use of a given expression, also similarity between two concepts (the donor subject and the recipient subject for which the verbal expression is sought) is contextually determined and may consist in abstract relations rather than attributive features." Verbal expressions of metaphors may undergo lexicalisation and are no longer experienced as metaphorical. Thus, the metaphor penetrates from the level of surface language to the level of lexical semantics. We will talk of lexical metaphor meaning lexical entities (single words, or phrases) affected by stabilised metaphorical changes of meanings. Lexical metaphors in the vocabulary of physics can be grouped into several sorts: A - reference extension; B - transfer of denotations, including catachresis with fantasy metaphor and metaphor based on mathematical analogy as its sub-species, and satellite metaphor; C - "imagistic paraphrase".

Kühn 1979: 409. Cf., for example, Verbrugge and McCarrel (1977) for the experimental corroboration of this view. See also footnote 141.

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A. Reference extension of an existing word lifts a single semantic restriction or a set of closely related semantic restrictions. It is a meaning redefinition (formal or non-formal) which makes a concept applicable to a wider range of phenomena than those to which it originally applied.92 Temperature originally referred to a sensible property of objects, coldness or warmth in relation to a certain standard measure. The identification of temperature with the average kinetic energy of particles disconnected the term from the bodily sensation, so that today, we can speak e.g. of "the temperature of the atomic nucleus" meaning the kinetic energy of nucleons. The initial basic attribute of temperature: direct sensibility, became irrelevant for the scientific application of the concept as temperature became incorporated into a larger and more comprehensive set of relations, forming a part of the kinetic theory of matter. Further examples of reference extension are "invisible light" and Huygen's notion of "sound wave". B. Transfer of denotations We use the notion "transfer of denotations" to denote an expression in which a single term referring to a donor subject becomes applied to a new kind of referent either on arbitrary grounds or on the grounds of theoretically irrelevant singular similarities (catachresis), or else on the basis of extended metaphors, including scientific models and outdated hypotheses (satellite metaphor). That means that we diverge from the convention in not using the expressions "catachresis" and "transfer of denotation" as synonyms. We will speak of catachresis as referring to a non-evolutionary event of a stipulation of meaning closing gaps in terminology93 by means of a transfer of a denotiation such that violates a whole network of semantic restrictions. "In such cases a member of the language community metaphorically transposes an established term from its typical setting to an atypical context".94 Because each lexicalised metaphor, including metaphorical extension of meaning leading to the modification (generalisation) of a concept, fulfils in one way or another the criterion often named as constituting catachresis - filling gaps in the existing vocabulary - we define catachresis additionally as such a use of a denotation which leads to polysemy. We distinguish between the following: (1) Catachresis which emerges in a novel act of juxtaposition between the reference of a given expression and the object to be named, based on single similarities (irrelevant from the point of view of the scientific theory) between the donor and the recipient and thus violating a whole network of relevant semantic restrictions. Similarities on which this kind of transfer is based are usually simpler than scientific analogies, and one needs no recourse to the theoretical knowledge of the donor subject in order to understand them. All knowledge of it that is needed belongs to everyday experience, that is, it is included in the general cornReference extensions can be rendered as metaphors in terms of a violation of a semantic restriction or, in an alternative formulation, following the general lines of MacCormac (1985), by arguing that they have two subjects between which the transfer of language takes place: the donor subject is the old concept designated with a given label (e.g. the old, material concept of "wave" or an indivisible "particle") and the recipient subject is the new concept, which is a modification of the old (the old one with some properties added or removed, or situated in other context). Catachresis can also produce "luxury metaphors" synonymous with already existing terms; this function we regard as marginal and we will refer to it only in passing in what follows. Rothbart 1988: 608.

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petence in a given language and general world knowledge. The similarity between the donor and the recipient subjects ranges as to degree of complexity from similarity of simple attributes such as size or shape, for example, to highly abstract concepts which can only be expressed in the form of complex multi-word descriptions. Similarities of simple attributes are exemplified by the terms "white dwarf" and "red giant", where the ground of transfer of denotation is their relative size (compared to the size of other stars); "electron shell", "electron cloud", and "butterfly effect", applied to certain subatomic phenomena on the grounds of shape similarities between the visual images of the involved phenomena and objects known from the everyday experience. Examples of relatively simple similarities of relations, based on analogies placing the subjects within two systems where an analogy holds between systems and the two referents of a denomination are related by occupying an analogous place in a system, are "radioactive parent" and "daughter product". Examples of highly complex similarities are the terms "bootstrap", "signature", and "virgin state".95 This type of catachresis is rather easily analysable in terms of meaning decomposition and re-organising semantic structure through re-topicalisation: topicalising the property constituting the ground of transfer. (2) Transfer of name from one physical measurable to another on the ground of mathematical analogy; it may be accompanied by conceptualisation of the physical measurable to be named as "a kind of" the donor measurable. (3) Fantasy-metaphors which are not motivated by similarities but simply assigned to their new referents on other grounds, such as charm, strangeness, beauty, justice, flavor of quarks. The other kind of transfer of denotations is satellite metaphor based on a scientific model or an established underlying metaphor, at the moment of its creation both novel and grounded in the existing frame of thought. Linguistic manifestations of underlying metaphors include spontaneously generated expressions, verbal cliches on the way towards lexicalisation, and expressions which have been lexicalised and are regarded as literal. This type of metaphor includes assimilative borrowings distinguished by their history as derived from false scientific hypotheses which then acquired metaphorical status. We call "assimilative metaphor" a metaphorical juxtaposition of two domains remaining from an earlier false scientific hypothesis consisting of a false categorisation as a result of an overstatement of similarity between two sorts of physical processes. We will speak of "assimilative borrowing" to denote such metaphorical expressions whose metaphorical status results from changes in scientific theory. What we mean is the evolution of meaning where polysemy is produced by a concept splitting into separate concepts as a result of the recognition that the diverse phenomena they refer to were mistakenly regarded as belonging to the same category. It is similar to stipulative linguistic metaphor in that it produces polysemy; it differs from it because it results from the process of the growth of knowledge and re-classification of experience instead of an act of stipulation of meaning. It is exemplified by the terms referring to electricity polysemous with terms of mechanics and with words from everyday language referring to movement and storage of matter. In common language, lexicalised satellite metaphors of extended metaphors are a border case between catachresis and extension of reference. Lexicalisations of expressions based on the "invisible", well-entrenched underlying metaphors of common language are frequently 95

All these terms are treated in more detail in section 10. 4.

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evaluated as generalisation of meaning of a given lexical item (reflected in dictionaries as multiple "shades" of the same general meaning) rather than as polysemous with the original meaning. In physics multiple words are also applied which have no formal definitions but are nevertheless an established part of the specialist's language through their collocation with defined terms, and which are to be classified not under terminology but as common language words" used technically on the basis of extended metaphors (e.g. an electron is "promoted" from one energy band to another). C. Imagistic paraphrases (stylistic metaphors) exist on the margin of terminology providing a simpler and more imagistic reformulation of complex scientific hypothesis: heat death, arrow of time. They enrich vocabulary providing additional options for verbal expression of physical ideas rather than remedy evident naming deficites. They possess imagistic contents which allows them to play some facilitating role in reasoning. This grouping is to be understood as a proposal rather than as a definite solution. A neat and non-controversial classification of metaphors in science, even of lexical metaphors alone, is made difficult by multiple interrelations between the general conceptual, the theoretical, and the verbal aspects of science, which make it possible to apply diverse criteria of classification. 3.3.2.3. Grammatical metaphor A specific kind of linguistic phenomenon which fulfils our criteria of the metaphorical is "grammatical metaphor", as conceived by Halliday and Martin (1993). The authors assume that the grammatical reclassification of words by means of derivational morphology constitutes the lifting of some of the semantic restrictions governing their application. From numerous aspects of grammatical metaphor, we have sorted out the nominalisation of adjectives and verbs as a process which shows a clear affinity with the notion of the "underlying metaphor" in general, and its sub-species, "ontological metaphor",97 in particular. We will present this affinity in the section dealing with the role of the underlying metaphor in the formation of physical concepts.

The new research in the field of LSP (Languages for Specific Purposes), especially in Germany, tends to withdraw the dichotomy common language-specialist language, and to work out a new, more adequate structure for various uses of language, based on the concept of "general language" (Gesamtsprache) providing the spectrum of linguistic resources from which particular sub-languages draw their means. Cf, for example, Hoffman 1985. We retain the terms "common language", "everyday language", "everyday speech" without implying that the above-mentioned dichotomy is a strong one; on the contrary, our study rather supports the "general language" view, showing that the same metaphors reappear in the specialist language of physics and in everyday speech (= common language); we retain the distinction to be able to point to the common ground. (It seems unconsidered to say, as it is sometimes done, that an LSP shares a property with general language if general language is the whole of language.) Traditionally referred to as hypostasis.

66 3.3.3. Functions 1. The contribution of metaphor to the discourse of physics takes parts on several functional levels: • denomination Scientific statements contain scientific terms, common language words, and common language words used technically,98 hence at the level of lexis we distinguish further between metaphor in - terminology - common language part of lexis

provides designations for physical concepts provides means of expression shared with common language

theory and concept formation

provides concepts, structures for systems of concepts, and physical models

scientific education

helps the acquisition of physical concepts by novices and non-experts

style

enhances vividness and compactness of rendering

meta-theory

shapes and expresses the selfunderstanding of physics

sociology of scientific research - motivation

marks the membership in the expert group

- organisation

suggests strategies and mobilises resources for certain lines of institutionalised research

In the discussion of "languages for special purposes" (specialists' languages) some authors, e.g. Benes (1968), differentiate between terminology and non-terminological specialist vocabulary; Schmidt (1969) divides specialist vocabulary into terms normed by fixed definitions, semi-terms which have no formal definitions, and "Fachjargonisms" such as "luxury" synonyms of defined terms. Our later analysis shows that the notions of a semi-term and of non-terminological specialist vocabulary in physics merge with our notion of common language word used technically on the base of a metaphor (metaphorical model).

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3.3.3.1. Denomination Terminology Transfer of denotations provides names for physical concepts, polysemous with names of concepts from everyday language or other branches of science including other areas of physics. Extension of reference of the existing terms and their corresponding concepts fulfils the need of remedying gaps of vocabulary by modifying the contents of these concepts and meaning of these terms. Common language part of lexis Defined terms in their usual form of nominal denotations are complemented by further linguistic means whose status as elements of specialist's language is not so clear. Some sorts of "invisible" metaphorical expressions of common language (lexicalised metaphors or expressions generated from common underlying metaphors) are applied in the same way in statements on physical processes as in other kinds of discourse. 3.3.3.2. Theory and concept formation Metaphors help to form scientific concepts and theories. This function of metaphor is closely associated with its denotative function, with the modification of concepts through extension of reference, with model-theoretical and imagistic functions. Transfer of denotations and concept formation Transfer of denotations is only partially separable from the function of concept formation. The relationship between this function of metaphor and its conceptual-theoretical function in the discourse in physics may be summarised as follows: In these cases where transfer of denotation is based on an extended metaphor, it contributes to the persistence of the conceptual relations incorporated in this extended metaphor. In the case of assimilative borrowing, where a concept is separated into two different domains as a result of the growth of knowledge, the conceptual assimilation of two domains has been the source of their sharing a denotation. The fact that different concepts still share the same denotation is usually accompanied by the fact that this assimilation persists in thought and helps conceptualise the less directly observable (visualisable) domain. The factor of primary importance for the question whether the transfer of denotations is accompanied by metaphorical concept-forming, theory-shaping processes is the type of recipient subject. Scientific concepts include fundamental and basic concepts such as mass, matter, or energy, providing a framework for presenting the major segments of the conceptual structure in the fields of physical science; theoretical concepts such as Carnot cycle, reversible process, diatomic molecule, which are capable of being given logically necessary and sufficient definitions; properties such as density or kinetic energy, which are capable of being given numerical degree and mathematical definition. In addition to these theory-relevant terms, other terms are necessary for the description of day-to-day activities of physicists, the so called "common concepts"99 representing things (e.g. materials, "natural kinds") and the experimental apparatus of science, including laboratory equipment, names "Cf. Strehlow 1993: 131.

68 of effects, and the like. Denotations of metaphorical origin can be found in each of these groups of terms. There are, however, differences concerning the amount of the conceptualtheoretical impact which can be associated with the metaphorical transfer of denotation to a theoretical concept or a mathematically defined property on the one hand, or to a "common concept" on the other. The issue of the conceptual-theoretical aspect of the transfer of denotation is relevant with regard to the theoretical concepts and properties, and negligible with reference to the "common concepts". Catachresis does not produce conceptual assimilation between the two domains of their reference but results merely in the establishment of additional new lexical entries for the same words or longer phrases. They are created in a single act of stipulation of meaning in spite of obvious significant dissimilarities between two subjects on the basis of isolated singular similarities between two subjects, e.g. shape similarity, or on arbitrary grounds, and are immediately lexicalised. This process is primarily lexical: the transfer of a lexical item from the usual type to a very different type of referents is not accompanied by any considerable degree of the transfer of conceptual structure. The conceptualisation of the recipient subject in terms of the structure of the donor subject which such a transfer of denotation may occasionally affect is marginal to scientific theorising, although metaphors of this kind may serve some psychological and sociopsychological functions for persons and groups involved in scientific inquiry. Reference extension and concept formation Reference extension provides ways of speaking about objects under investigation, modifying, that is, generalising, the meaning of the existing concepts. Extensions of reference of existing concepts into new domains may be suggestive of physically significant aspects of these new domains (that is, they may turn out to be based on physically significant shared characteristics between the donor and recipient domain) and lead to the modification of an existing category and its associated concepts. This is a case of filling gaps in the existing vocabulary by means of a stipulative metaphor which, in contrast to catachresis, produces the change of meaning of a concept instead of polysemy. This process is to some extent the reverse of what we called assimilative linguistic metaphor, where an initial hypothesis was disconfirmed and a domain containing a given concept became recognised as heterogeneous. Examples are the wave concept as applied for the first time by Huygens to propagation of sound and the notion of invisible light.100 Extensions of reference exert an impact upon the construction of scientific theory because they suggest and stabilise new saliences by pointing to similarities and analogies between two domains and pinning them down in a linguistic expression, which constitutes a part in the process of restructuring concepts. They consist of such applications of verbal expressions to new sorts which, if they acquire stability, cause shifts in the semantic structure of verbal expressions - the shifts in their semantic fields. The new referents are initially perceived as significantly similar to their usual referents, but the application of a verbal expression nevertheless violates to a considerable degree the semantic restrictions upon their standard use. 100

MacCormac (1985: 84) speaks of "metaphors which have often been confirmed by experience", and states that "if a confirmation occurs over and over again, and the metaphor becomes commonplace, then a new category of ordinary language occurs; this new category arises from the combination of two categories previously not assocciated" (ibid.: 56). "Reference extension" is our term for the process he is referring to.

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Once applied, reference extensions often initiate developments confirming their new semantic hypothesis (that neglects the restriction(s) in question) by showing that the ground of the transfer was a more significant physical aspect of reality than the difference constituted by missing versus exhibiting a property corresponding to the violated restriction. They are produced to close gaps or to enrich the vocabulary or to simplify the description of the recipient subject, and result in the change of meanings through the assimilation of the two subjects on conceptual, theoretical, and linguistic levels. The shift of meaning of one expression produces further shifts within its semantic field. Imagistic function is performed by metaphors which make possible the generation and interpretation of abstract concepts in terms of sensorial analogues, i. e. such properties as belong to concrete objects. A metaphor makes an abstract relationship or a set of abstract relationships graspable by pointing to an immediately comprehensible image. This aspect of metaphor is closely related to its model-theoretical function because theoretical models are frequently representations of the more abstract in terms of the material and visualisable. It is, however, not exhausted by it because metaphors also help to form images for simple pre-theoretical concepts (e.g. time). "Imagistic" is not to be identified with "pictorial" - there are different kinds of sensory images; however, visual images are the prevailing kind, just as vision dominates other senses as a source of non-linguistic information, and the images in physics are mainly if not exclusively of this kind. There are different kinds of images associated with scientific metaphors. Some of them are merely individual and subjective. They may be helpful to a scientist whose cognitive capacities depend to a large degree on visualisation, but are not essential to the comprehension and linguistic formulation of metaphor. For example, the application of the clock metaphor in reasoning about the world may have been supported by a visual image of a clock, but not necessarily so - what counted was the set of abstract categories acquired from the clock as the donor subject. Studies of imagery among scientists showed that the degree of visualisation is an individual matter. Some expert physics problem solvers depend strongly on visualisations101 (as e.g. Faraday, Maxwell and Einstein did),102 and often first generate dynamic images before working with equations and laws; others do so hardly at all. Visualisation finds a language-independent expression for example in the gestures accompanying the description of physical processes. Transfer of names often depends on a visual image of the recipient subject: of such an origin are, for example, the expressions butterfly effect, black box, white noise, seesaw effect, spin of a particle. In some pedagogical metaphors, the visual image is the tool of understanding, in the sense in which Hesse speaks of the explanatory role of metaphor in science: it gives cognitive satisfaction through offering a familiar substitute for a highly abstract concept which can alternatively be grasped only in mathematical terms. Such is, for example, the image of an expanding balloon with celestial bodies modelled as patches on its surface, used in explaining to non-experts (non-mathematicians) how the universe can have no centre but still expand in all directions (cf. Lightman 1989). 101

102

Cf. Hoffman 1985:342.

Cf. Dreistadt 1968 and Walkup 1965.

70 Finally, some metaphors constituting theoretical concepts depend inherently and in an intersubjectively shared way on visualisation, which constitutes the basis of naming and of conceptual manipulation, such as the band theory of solids or the metaphor of light travelling, which is an indispensable basis of geometrical optics, expressed in the visual presentation of its laws (drawings). Model-theoretical function is performed by metaphors through their contribution to scientific models based on conceived analogies between a domain to be accounted for and another domain taken from another context, typically from another branch of physical science. The relation between metaphors and scientific models is a matter of verbal controversy: scientific models are included by some in the notion of metaphor; sometimes it is said that models are based on metaphors or that they are expressions of underlying metaphors, sometimes the name "model" is reserved for the non-verbal theoretical structures and the name "metaphor" is applied to the linguistic expressions resulting from these structures. The words "metaphor" and "model" are often brought together without differentiation in the context of the analysis of the role which analogical thinking plays in scientific theorising. We will assume that analogical models are based on novel metaphors: whereas the initial, holistic juxtapositions of two domains may be classified as metaphors, analogical models result from the selection of the elements and characteristics within the donor domain, which can be applied in the recipient domain, and working out non-ambiguous, systematic mapping between this selected set of elements and characteristics and a set of elements and characteristics within the recipient domain. Apart from analogical models, scientific models can also be based on non-novel, wellentrenched underlying metaphors in the sense of Lakoff and Johnson (1980), such as spatialisation metaphor. Explanatory function of metaphor should be mentioned here, even if it is rather self-evidently contained in the concept-shaping, model-theoretical, imagistic, and educational functions because it is frequently referred to in the literature: "metaphorical redescriptions" produce accounts of physical facts which are cognitively satisfying because they provide sense of familiarity. This description of the explanatory function of metaphor by Hesse (1966) was a novelty not only because it threw new light upon metaphor but also because it was a "psychologistic" amendment to the prevailing conceptions of scientific explanation, which were defined not in terms of their (subjective) cognitive relevance for the human subject but solely in "objective" terms, such as reduction to events on a (more) basic level or proving that a given event is necessary (in the determinist account of nature) or possible (in the statistical account) consequence of, roughly, the sum of a scientific law plus the given initial and boundary conditions. 3.3.3.3. Education Metaphors help novices and non-experts to acquire physical concepts. In the discussion of the function of metaphor in physics, the distinction has frequently been maintained between theory-constitutive and exegetical or pedagogical function, or theory-constitutive and educational metaphors:

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Theory-constitutive metaphors constitute "an irreplaceable part of the linguistic machinery of a scientific theory".103 Their contribution to the discourse of physics takes place on the level of theory and concept formation; they are used by scientists to express insights and claims for which no literal paraphrase is known. Such metaphors, according to Boyd (1979), invite the listener/reader to explore similarities and analogies between the characteristics of the primary and the secondary subject, including such as have not yet been discovered, and suggest guidelines for further research. The criteria proposed for defining the theory-constitutive metaphor are, then, its non-paraphrasability and the role it plays as a guide to further discovery. The theory-constitutive aspect of metaphor is usually discussed in the context of analogical models. However, theory-constitutive metaphors include both structured systems - analogical models - and simpler, more primary conceptualisations, such as the concept of force or the concept of light as a moving object presupposed in the rules of geometrical optics. Exegetical and educational function is performed by metaphors applied in teaching or explaining theories which can already be formulated, at least to large extent, without their application. Theory-constitutive metaphors sometimes turn into pedagogical metaphors after they have received an independent reformulation. The most frequently cited examples are the solar system as a model of an atom and the billiard-ball model of gases; that is, scientific models and analogies which emerged out of an anticipation of an analogy between the donor and recipient subject, an analogy which has been exploited before now to the point at which its scope is known and can be redescribed in independent terms. They form an established set of metaphors constantly re-appearing in handbooks and popular expositions of scientific concepts. Besides, numerous new metaphors are introduced at particular occasions in the popular scientific expositions of physical ideas, where they substitute rather than complement more formal instruction. 3.3.3.4. Style Stylistic, or rhetorical function: metaphor provides paraphrases for concepts and hypotheses which can be formulated in independent terms, expressing them in the language which is more imaginative, introducing connotations binding them to the human sphere, and also providing means to express complex states of affairs in simpler linguistic form. In talking of the "stylistic" aspect of metaphor, we refer here to cognitive diversity of linguistic expressions with respect to the degree of visualisability, concreteness vs. abstractness, intuition of familiarity, emotional load, and relatedness to other domains of experience. If we replace an utterance formulated in abstract theoretical terms only by one containing "time's arrow" or "Maxwell's demon" or the expression "the electron has an itch to leave", all these factors change so that the cognitive impact of this utterance is also different. This difference we refer to as stylistic. This function is performed by metaphors which we call "imagistic paraphrases", such as, for example, Maxwell's demon, arrow of time, and cosmic death. Such metaphors replace or augment the formulation of theoretical insights in the exact sciences in a language which is closer to everyday language than a formulation consisting of theoretical terms. They do not contribute to the structure of the scientific theory, but redescribe scientific theories in terms Boyd 1979: 360.

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of concepts which are imaginative and generally understandable; in this way, they perform an exegetic function and often become an attractive source of inspiration for the humanities, stimulating the creation of links between exact sciences and humanities as two domains of creative discourse. Through their imagistic content, this type of metaphor can also play a facilitating role in reasoning about theoretical issues (e.g. Maxwell's demon). Because such metaphors, even if they do not count as scientific terms, are unambiguously and precisely translatable into statements based on physical terminology, no ambivalence, imprecision or ambiguity results. 3.3.3.5. Meta-theory Meta-theoretical function is performed by metaphors structuring and articulating the approach to the object of knowledge in general and of physical science in particular, the view of the aims, objectives, and possibilities of science; defining the kinds of questions which can reasonably and meaningfully be asked; in brief, informing the self-understanding of scientific research. 3.3.3.6. Sociology of scientific research Motivation The sociolinguistic function is performed through the contribution of lexical metaphors (denotative terms) to the "Fachjargon" (specialists'jargon) - an "insiders' code" - shared by practising physicists, marking them as a professional group, giving them the feeling of intimacy with the subject matter as well as with colleagues, and distinguishing them from non-experts. The sorts of metaphors which contribute particularly effectively to this function of supporting "expertism" in physics are: "Werkstattmetapher" - denotations for the equipment used and effects observed in experiments conducted in the physical laboratory, and fantasy metaphors. The sociological function of metaphor as a marker of group membership is particularly apparent in the case of a "luxury metaphor" - an additional denotation for a concept (e.g. an instrument or an effect) synonymous with an already existing "official" (dictionary) term. In what follows we will not pursue this function of metaphor any further, as our subject matter focuses upon the "form and contents" of metaphors rather than the affective circumstances of the physical discourse and the scientist as a person. Organisation The growth of interest in metaphor and analogical reasoning as the means of accommodating new knowledge and leaping forward towards new insights is due to the failure of the inductive theories of scientific discovery. This failure also triggered the development of approaches towards theory making which decentralise the issue of the logical structure of scientific theories in favour of treating scientific research as primarily a sort of social activity. The very possibility of drawing a border line between the social and the cognitive factors in scientific research is called into question. A representative of the "anthropological" conception of science, Knorr-Cetina (1984) reformulates the objective of a research scientist as finding out a strategy of local success - which is a social as much as a cognitive category - rather than the Truth, and regards metaphor and analogy (defined in terms of the primitive

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notions of similarity and distance) as means by which solutions to problems are found before rather than after procedures are designed that "make them work". Casting their light behind rather than ahead, metaphors and analogies serve as guides in devising chains of practical steps connecting the problem and the already provided solution. They mobilise resources and capacities for certain lines of research which, even if they also frequently end in failures, have a relatively high probability of success because it is more promising to start with a potential solution at hand than with an open problem, and because the concepts they utilise in a new context have already proved successful before. The transferred idea is "made to work" through the reconstruction of whatever may be needed in order to make it part of the social process of "manufacture of knowledge" in the new context, rather than through a mere prospectively "testing a hypothesis". In this approach, figurative and non-figurative analogical reasoning are treated with the view to the turns they give to the social processes constituting modern institutionalised science rather than to their internal conceptual and linguistic structure. It could be illuminating to apply Knorr-Cetina's method to a closer analysis of this structure: to observe and analyse the origination and use of metaphors in the physicists' laboratory, in the informal exchange of thoughts between experts, on their way from "first ideas" into publications and to the status of the established resources of science. As we have no opportunity to conduct such observation, and because we are interested in the abundant instances of metaphor in the past which are not available for this kind of study and can only be analysed on the basis of written records, the "anthropological" thread will not be pursued in this work.

Part Two: Metaphors in Physics

4. Underlying metaphors of everyday thought in meta-theory and the concept formation of physics As a branch of human intellectual activity, physical research and theory-making proceed in the mode shaped by the pre-scientific ways of conceptualisation, which are dependent on the resources made available by language as a meaning-making device. Metaphorical processes in physics start on the level of ordinary language and their analysis must start from that primary level at which language makes reality accessible to conceptual manipulation. In this section we will deal with some basic kinds of metaphor which enable us to structure our experiences: hypostasis, spatial metaphor, anthropomorphism and organification. We will have a close look at their influence upon the emergence of some scientific notions and hypotheses. All those kinds of metaphor are conceptual metaphors secondarily expressed in language. The function of verbal "satellite metaphors" is to express the underlying conceptualisation; their side-effect (culminating in lexicalised expressions) is to stabilise the conceptual metaphor from which they have been generated. The latter is made to look self-evident, so that sometimes it is difficult to perceive it as just one of the possible conceptualisations (rather than as a matter of fact). This disadvantage of metaphors as potential obstacles to the conception of reality in other, possibly more fruitful, ways is counterbalanced by the ease of usage of the elements of reality with which they provide us: we do not have to anatomise everything anew every time we want to make an assertion about a new experience. The occurrence of those kinds of metaphor is not peculiar to scientific enterprise: they are commonplace in thought and language. Through their consideration, we want to stress the continuity between the resources provided by everyday language and conceptualisation on the one hand, and the scientific language and concept formation on the other. The impact of those sorts of metaphorical processes will be exposed insofar as it is relevant to the issues of theory and concept formation, as well as meta-theory and methodology of the physical science. A more extensive presentation of their contribution to physical terminology will be postponed to section 10. 4., dealing with metaphorical transfer of denotation.

4.1. Hypostasis 4.1.1. Nominalisation as metaphor Nominalisation of adverbs, adjectives and verbs (e.g. to fall) is a conceptual and linguistic device making relations, properties and processes (e.g. a fall), which exist only as abstractions from perceptual sequences, accessible to a similar kind of analysis as the one applied to substantial entities. It changes the conceptualisation of relations, properties and processes and allows them to enter into such semantic relationships with other aspects of the

76 situations being the object of the conceptual and verbal representation which are typical of entities. Heller (1970) and Halliday & Martin (1993) point to the role of the grammatical mechanism for nominalisation (the article) in Greek in the development of abstract thought. Havelock (1983: 14) states that the conceptual task of the Pre-socratics, the originators of our scientific vocabulary, "required the elimination of verbs of doing and acting and happening ... in favour of a syntax which states permanent relationships between conceptual terms systematically". He cites Heraclitus suggesting that "is" (esti) should replace all verbs.104 The scientific Greek from about the 5th - 6th century B. C. used on a massive scale the transcategorising potential of the derivational morphology to generate sets of abstract technical terms from words designating properties and processes, such as change, rest, motion, distance, or revolution. More than anything else, the two potentials of grammar: that of turning verbs or adjectives into nouns, and that of expanding the scope of the nominal group, opened up a discourse for technology and the foundations of science. Two notions belonging to different research perspectives are available for the analysis of nominalisation as metaphor: - ontological metaphor (Lakoff and Johnson 1980: cognitive semantic approach); - grammatical metaphor (Halliday 1985, Halliday and Martin 1993: functional grammar approach). From the perspective of cognitive semantics, nominalisation is the most rudimentary, that is, minimal kind of ontological metaphor. From the perspective of functional grammar, nominalisation is a species of grammatical metaphor characterised by the incongruence of the semantic content and its grammatical realisation. It is a grammatical transcategorisation by means of morphology accompanied by a conceptual transcategorisation of the elements of experience. 4.1.1.1. Ontological metaphor Ontological metaphor is the kind of conceptual transformation which allows us to understand various kinds of experience in terms of concrete objects and substances. The capability of such conceptualisation constitutes the cornerstone of abstract thinking. The ontological metaphor allows us to conceptually manipulate components of our experience, including processes, events, attributes, and relations, by treating them as entities. The conceptual and linguistic operations made possible by ontological metaphor are those typical of our dealing with things and substances: categorisation, quantification, identifying particular aspects, treating as a cause, etc. Processes, events, attributes and relations conceptualised and linguistically realised as entities can be referred to for their own sake, that is to say, they can be focused upon and made the subject of an utterance, treated as an agent, or as an object of a predicate. Our experiences with physical objects, including our own bodies, provide the basis for ontological metaphor. The ontological metaphors impose different degrees of structure upon their primary subject, that is to say, their donor domains are more or less specific: from a mere entity (hypostasis) to an entity of a specific type (e.g. "inflation is an enemy"). Nominalisation is the most basic form of ontological metaphor because it lends to its subject only the most general properties of a thing. It provides a conceptual basis for a 104

Havelock 1983: 25.

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further metaphorisation in which the nominalised concept may undergo a metaphorical elaboration lending it the structure of another thing serving as a secondary subject (e.g. state as a container, electricity as a liquid). 4.1.1.2. Grammatical metaphor The core of the concept of "grammatical metaphor" is the notion of congruence between the semantic contents and the grammar applied in its surface linguistic realisation. A "congruent" relationship is a "natural" relation between semantic and grammatical categories. Examples of congruent types of relationships between semantics and grammar are quality adjective, thing - noun, action - verb, incongruent: thing - process, quality - adverb, logical relation - verb ("results from" instead of "because", "so") etc. Congruence (versus incongruity) is gradual rather than absolute: an example of congruence gradation in the ascending order is the sequence capability -»· capable ->· can. This sequence shows that, similar to the case of the lexical metaphor "dead" in the process of language development and capable of functioning as a "literary paraphrase" of a metaphorical expression or else as a donor subject for another level of metaphorisation, grammatical metaphor expands the potential of a grammar recursively - the more congruent grammatical realisation is not necessarily a basic (non-metaphorical) one. On what grounds does "grammatical metaphor" qualify as a metaphor? The question pertains to the issue of defining the difference between metaphorical and literary meaning. Even those researchers who emphasise that the difference between literal and metaphoric is relative and gradual rather than absolute and categorical, agree that the literal is to be regarded as the more basic, primary level of communication. Halliday & Martin (1993) name as pragmatic criteria of basicness - the prevailing acquisition order, - the order of occurrence in the history of a language, - the prevailing order of occurrence in a text. The latter criterion for treating nominal expressions as secondary, that is, metaphorical, comes to bear whenever the process of nominalisation is made explicit by the pre-occurrence in the same text of an alternative wording (adjective, verb) for the process, event, or property in question, more congruent with the corresponding semantic contents. Consider the following fragment of an early scientific discourse: Let us now stop the paper at the focus G, where the light appears totally white and circular, and let us consider its whiteness. I say, that this is composed of the converging colours. For if any of those colours be intercepted at the lens, the whiteness will cease and degenerate into that colour which ariseth from the composition of the other colours which are not intercepted. And then if the intercepted colours be let pass and fall upon that compounded color, they mix with it, and by their mixture restore the whiteness .. .'°5 [...] The paper I had first placed so that the image might appear white ... the whiteness ... did change into a colour; these colours succeed one another ... there appeared a perpetual succession of colours ... the appearance of the single colours ceased, (emphasis HP)106

Here, the terms "whiteness", "composition", "mixture", "succession", and "appearance" are nominalisations that bridge the preceding and the following part of the argument. They con105 106

Newton: Opticks, 1717, 1952: 433. ibid.: 434.

78 stitute the "given" of the clauses they appear in; instead of repeating what has already been said, the author can proceed from them to the further part of the unfolding argument. In this way, parts of a preceding argument may be packaged into grammatical and conceptual forms, making possible a development of a chain of reasoning. Nominalisation allows us to compress a complex phenomenon into a single semiotic entity by making it one element of the clause structure, and use it as a point of departure for the following message. It opens a vast potential for distributing and redistributing information within a sentence, particularly the rhematisation of the parts of the preceding discourse. From the time of Newton to the present, scientific discourse has evolved towards a form of a sentence characterised by objectification of events and qualities, accompanied by the expansion of verbs used to relate parts of argument, such as represent, explain, prove, follow from, constitute, correlate, lead to, result from, correspond, arise from, etc. These two devices coupled together largely increased the argumentative potential of a written discourse. 4.1.1.3. Nominalisation of science and the scientific vision of reality The "nominalisation of science" did not remain without influence on the scientific reconstruction of reality. In nominalisation, which is among the most characteristic kinds of grammatical metaphor to be found in scientific discourse, the prototypical realisation of a process (verbs) and the prototypical realisation of a property (adjective) come to be reconstructed in the form of the prototypical realisation of a thing (noun). Viewing a process or a property as an entity allows us to identify a particular aspect of it, quantify it, etc. Nominalised expressions are not usually regarded as being metaphorical. One reason for that is that the nominalisation itself does not endow its object with additional semantic properties above and beyond the general properties of a thing. Halliday and Martin (1993) show that the grammatical metaphor was an important means towards the development of the argumentative structure of scientific discourse. At the same time, if we accept the premise that language is a meaning-making rather than merely a meaning-expressing device, we are led to the insight that this adaptation of language to the construction of scientific discourse resulted in a construction of reality which is of a particular kind: object-based and stable, rather than process-based and temporary. This tendency is enhanced by the process of technicalisation which often follows the formation of nominal expressions. In the above-quoted fragment of a scientific text, the nominal isations are used in a pre-technical sense as grammatical devices to push the argument forward. This lexicomorphological process is the first step towards the establishment of abstract technical terms which enter physical theories and become elements in their defined systems of interrelated meanings. In the Definition III of Newton's "Principles", we read: The quantity of motion stays the same ... the motion of the whole is the sum of the motion of all its parts.

Here, the original semantic status of motion as a process is replaced by an abstract theoretical entity no longer synonymous with its original meaning - motion is no longer synonymous with moving. In the process of abstracting moving into motion (through nominalisation), moving becomes a substance and may be subjected to a conceptual manipulation

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characteristic of substances: divided, added, and quantified. Made into an entity as a kind of state, the process of moving appears more static, that is, compatible with the world of entities and amenable to it. Nominalised motion belongs to the world kept still so that it becomes accessible to inspection. Thus, the nominalised expressions result in the establishment of fixed technical terms (motion, radiation, attraction, etc.) constituting a further enhancement of the thing-based meaning structure of language and conceptualisation of experience. Isolated examples of such a process would be of no importance, but, when happening on a massive scale, they exert a vast influence on the way of conceptualising reality as an aggregate of entities. The picture emerging out of the nominalised scientific discourse is that of reality persisting through time rather than changing with it - which is a prototypical property of a prototypical referent of a noun. Nominalisation is a device used to hold reality still in order to make it accessible for experiment and reflection. The adaptation of language to the needs of scientific argument resulted in the development of a new style of wording, which constructed a reality of a particular kind: fixed and determinate, predominated by objects. 4.1.1.4. A physicist's critique: Bohm's "rheomode" The direction of physics in the twentieth century has been rather opposite to the process referred to in the preceding section: moving from thing to process, from stable to flowing, from determinate to probabilistic, from fixed to relative. This divergence between the means made available by language and the way of seeing adequate to the demands of developing trends in scientific thought has resulted in a rise of new language criticism. According to a physicist turned philosopher, David Bohm, language is helping to bring about the fragmentation of processes, dividing them into separate entities. In the scientific view inherited from the centuries past, the world is constituted out of a set of basic particles (entities) of fixed nature. Bohm (1980: 29) proposes a change in the syntax and grammatical form of sentences that would give a basic role to the verb rather than to the noun: This would help to end the sort of fragmentation indicated above, for the verb describes actions and movements, which flow into each other and merge, without sharp separations or breaks. He proposes a new mode of language which would be adequate to the idea of the "wholeness" of the universe and in which apparently static and separately existing things are seen as relatively invariant states of continuing movement.197 He gives this mode a name: a rheomode ("rheo" coming from a Greek verb meaning "to flow"). It should be an experiment in the use of language concerned with trying out whether it is possible to create a new structure that is not so prone toward fragmentation as is the present one. '* "Rheomode" would be based on verb root forms. Bohm proposes to introduce a set of rules for the formation of new words out of "basic" forms, that is, verbal ones, with the following effect: 107 108

Bohm 1980: 30. ibid.: 31.

80 Actually, the relationship between parts of a word may, in general, be of much the same sort as those between different words. So the word ceases to be taken as an indivisible atom of meaning and instead is seen as no more than a convenient marker in the whole movement of language, neither more nor less fundamental than the clause, the sentence, the paragraph, etc.109

Bohm is dissatisfied with the way language fails to meet the demands of the new dialogue with nature. His objective is the creation of a language that would represent the flux of things and reconstruct the dynamic character of experience. The idea is by no means new: in Plato's "Timaeus" (1937,2: 449), we find a fragment stating that since elements are perpetually changing into and out of one another and have in them nothing permanent, they should be called not 'this' or 'that', but always 'such'. Anything which we see to be continually changing, as, for example, fire, we must not call it 'this' or 'that', but rather say 'that is of such and such a nature'; nor let us speak of water as 'this', but always as 'such'; nor must we imply that there is any stability in any of those things which we indicate by the use of words 'this' and 'that', supposing ourselves to signify something thereby; for they are too volatile to be detained in any such expressions as 'this' ... or any other mode of speaking which represents them as permanent.

And at the beginning of this century, Mauthner (1913: 489) stressed the fluent, processive character of the world saying Unsere Worte oder Artbegriffe ... scheinen uns so zuverlässig zu sein, daß mancher den Kopf schütteln mag, wenn er auch so handgreifliche Begriffe wie Erde, Wasser, Eiche, Mensch für Hypothesen halten soll. Wie aber, wenn wir uns einen Geist vorstellen, für den Millionen Jahre der Entwicklung wären wie ein Tag? Wie, wenn vor den Augen dieses Geistes die Urstoffe der Welt in wenigen Stunden seiner Zeitrechnung gemächlich zu der Erdkugel sich ballten, glühten, erstarrten, lebendig würden, erfrören, zurückstürzten in die Sonne und sich in ihrer Glut neuerdings auflösten in die Urstoffe der Welt? Ist dann der Begriff Erde, der Name der Form eines flüchtigen Viertelstündchens, auch noch mehr als ein luftiges Wort? Ist dann der Name Erde noch mehr als die Hypothese eines Übergangszustandes der Stoffe? Ist dann der Name Erde noch mehr als die Hypothese ,sieden', die wir von einer Übergangsform des Wassers gebrauchen?

Scientific language developed in a direction contrary to that advocated by Plato; as a result, it is experienced as not being a satisfactory means to articulate the process-centred tendencies of contemporary physical science. Bohm's simplistic suggestions make manifest the sense of incompatibility between the old language and the new view of reality to be encoded. To some extent, this may be regarded as a contemporary counterpart of language criticism of the seventeenth century concerned with making language adequate to the emerging requirements of experimental science. Just as the seventeenth century scientistphilosophers demanded the purification of language from the metaphoric distortion, the contemporary criticism postulates the modification of the object language because of its lack of correspondence to what is taken to be real. In a way, however, the particular reasons for the contemporary physicist's dissatisfaction with language appear to be contrary to those that motivated the demands of language reform by the early scientists. Contemporary scientists find language inadequate to express the insights of physics, or "translate" mathematical formulas, because of its rigidity and precision which blocks the creation of new semantic entities. Applying semantic units in a context 1OT

ibid.: 41.

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widely different from that in which they originated, the physicist is still bound by the original semantic rules: "we should have no language if we did not keep to the rules".110 The language of mathematics with its system of arbitrarily introduced symbols allows us to overcome the restrictions of the established semantic rules and thus makes the description of new insights possible; but these insights often cannot be expressed in natural language, not even in the specialised and technical language of physics, because of its semantic inertia which is exactly what makes it serve its function as the means of communication."1 Whereas in the seventeenth century the natural philosopher criticised natural language for "metaphorical imprecision", the contemporary physicist is dissatisfied with it because of its excessive morpho-syntactic, syntactic and semantic rigidity. 4.1.2. Hypostasis and the emergence of a scientific hypothesis: electric fluid In the preceding section we pointed out the tendency of modern science to treat processes in terms characteristic of entities and the dominance of the thing-language. We hold language to be a factor in the concept formation and not merely the means of expressing concepts, and assume that the dominance of thing-language, resulting to a large degree from the discoursecarrying technique of nominalisation, exerted an influence upon the emergence of such notions as electric or heat fluid. In Toulmin's wording, "there are indeed many phenomena in accounting for which we come to think of the grammatical subject as having a physical counterpart". The way from the experience of hot and cold, or objects moving towards an electrified glass rod, toward the notion of heat and electricity as fluid substances transported from one physical object to another was by means of objectification (hypostasis) of the "grammatical" subject of statements such as "Heat flows from A to B" or "The electrical faculty has been passed from X to Y". The examination of the language of "electricity", as the eighteenth century physicists used to call the science dealing with electrical phenomena, illustrates the point in question: it shows how the mere phenomenological description of phenomena shifted in the direction of substantiality being attributed to the notion of "electrical faculty". In the descriptions of the electrical attraction from its early beginnings, there is more than pure description in many of the early records of the amber effects. It is frequently said that amber "attracts" or "drags" light objects, thus projecting upon it the role of an agent in the process of light bodies moving towards the electrified amber, in an implicit attempt to explain the observed phenomena. The word "electric" was probably coined by William Gilbert to name such substances which, subjected to friction, "behave" like amber "drawing" light object to themselves; the adjective identified the process as due to a property common to amber and some other substances conceived as agents in this process. The nominalised form, "electricity", probably first appeared in Sir Thomas Browne's "Pseudodoxia epidemica" in 1646. In 1647, Robert Boyle (1980: 252-255) offers the following description of the experiment he is going to conduct with "electrical bodies": 110 111

Hütten 1958: 178. A good illustration of this inertia is the failure of the "wavicle" concept, proposed first by Eddington in an attempt to overcome the difficulties of the wave/particle duality of quantum theory. It turned out to be inapplicable because of the lack of semantic rules governing its use which would provide a basis for constructing a language system.

82 What bodies are electrical and what not ... [...] To measure the attractive power of Electrical Bodys by a nice pair of scales ... [...] To try whether the extract of red Amber will be more electrical than the Amber itself was and whether Amber unbroken being infused in pure spirit of wine often renued till the Liquor will yeeld no more tincture, the remaining Lump will have its electrical virtue lessened, encreased or neither [...] Whether the Colophony ... be Electrical, and more or lesse so than Amber it self was ... [...]Whether the various manners of nealing Glasse ... will encrease or diminish the Electricity of it... [...] Whether Glasse made hot will retain all its Electrical facultie, or any part of i t . . . [...] What kind or measure of friction does give an Electrical) Body its highest power of attracting ... [...] Whether an Electrical Body will retain its attractive virtue ... (emphasis HP)

In this account, the "electrical virtue" or "faculty" appears as the grammatical and ontological metaphor derived from the adjective "electric", which is itself a grammatical metaphor, a short-hand note for the observed phenomenon of light bodies moving towards the "Electrical Body" after it has been subjected to friction. The adjectival construction "more electrical" finds a nominalised counterpart in the notion of "electrical virtue lessened increased". "Electrical virtue" appears here as a stylistic variation of the notion of a body "being electric" and is used interchangeably with the notion of "attractive power", itself an ontological metaphor developed out of metaphorical "attract", the latter being based on the projection of the agent role onto the process of light bodies moving towards the electrified amber."2 In what follows we will pursue the next step in the development of "electricity" in order to see how nominalisation applied to the observed facts helped procure a scientific hypothesis - one of several "imponderable fluids" of the early modern physical theory. In 1729, S. Gray conducted his famous experiments on conduction and electrification by influence. That year, he made public an important discovery: the "electric virtue" of a rubbed glass tube can be transmitted to other bodies with which it is in contact, so as to give them the same property of attraction as the tube itself had. In Gray's description of his experiment, we read: ... whether ... the electricity would be carried down by the line to the ball ... [...] the electric virtue passed from the tube up the pole ... [...] I concluded that when the electric virtue came to the loop that was suspended on a beam ... [...] The line on which the ivory ball was hung, and by which an electric virtue was to be conveyed to it by the tube ... [...] Then the cane being rubbed, and the leaf-brass held under the ivory-ball, the electric virtue passed by the lone of communication to the other end of the gallery, and returned back to the ivory ball."3 (emphasis HP) What can be observed is more or less like that: after a glass rod, on which some operations have been performed which (tentatively) caused small objects to move in its direction, has been connected by a wire to an ivory ball, small objects put in the vicinity of the ivory ball 112

113

At the same time, Boyle actually believes the attraction to be caused by a substantial agent, the effluvia which "fasten upon the body to be drawn, and that in such a way, that the intervening viscous strings, which may be supposed to be made up of those cohering effluvia are, when their agitation ceases, contracted or made to shrink inwards, towards both ends ..." Grey, quoted in Roller and Roller 1954: 31-35.

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begin moving towards it. In Gray's account, the grammatical subject of all the verbs of movement is the electric virtue. As we see, to re-describe the experiment in an "observation language", to transform the description above so as to avoid the notion of an electric virtue being transported, or conveyed, from one electrified object to another, re-writing it in a process-language based on the description of the behaviour (movement) of the observed bodies rather than on the nominalisation "electric virtue", is a rather cumbersome linguistic procedure. The notion of transporting or conveying "electric virtue" in this paragraph seems to be of a purely phenomenological character, not involving any claims concerning the substantiality of the cause of the movement of small objects towards the ivory ball. Gray does not use the term "electric fluid" or "electric substance". The verbs "come", "convey", "return", and "pass by" are applied here metaphorically (in the sense of Lakoff and Johnson 1980) and are provided with grammatical support by the nominalised notion "electric virtue", neutral with respect to the issue of the grammatical subject having a physical counterpart, i.e. neutral with respect to the question whether there is a substance being transported along the conductor line. In numerous later accounts of electrical conduction, the grammatical subject of these verbs comes to be associated with a material counterpart; that which "passes" and "returns" becomes not only conceptualised as a thing but is also taken to be a thing - an electrical fluid, whose physical nature becomes a subject of inquiry. This gradual emergence of the fluid theory of electricity illustrates the psychological progression from a grammatical substantive to the hypothesis of a substance, and confirms Friedrich Lange's (1913: 559) contention that Indem wir das Ding Schritt für Schritt auflösen, bleibt uns immer der noch nicht aufgelöste Rest, der Stoff, der wahre Repräsentant des Dinges. Ihm schreiben wir daher die entdeckten Eigenschaften zu. So enthüllt sich die große Wahrheit, kein Stoff ohne Kraft, keine Kraft ohne Stoff, als eine bloße Folge des Satzes ,kein Subjekt ohne Prädikat, kein Prädikat ohne Subjekt'.

4.1.3. Hypostasis and the constitutive metaphor of optics: travelling light The concept of light travelling is an "invisible metaphor" of everyday language which penetrated into physical theory: it is not a specific product of scientific research because light has "always" been spoken of in terms of movement - as entering a room, falling or thrown upon an object, etc. - in everyday language without any dependence on scientific theory. This is manifest in the linguistic-conceptual contradiction in Aristotle who, at one point, rebukes another philosopher for speaking of light travelling, reminding us that light is only a property or state of a medium, but who himself asserts elsewhere that it travels in straight lines.114 And, some two thousand years later, in the fragment from "Opticks" where Newton declares he is using language neutrally with respect to whether light is propagated in an instant,"5 (i.e. requires no time for becoming simultaneously present in two distant places), or travels with a finite velocity, but speaks anyway of light rays being stopped and let pass, "refracted or turned out of their way in passing from one transparent body ... to an114

115

Sabra (1981: 39) claims that "Aristotle censured Empedocles for having spoken of light as travelling". In "De anima" and "De sensu", light was characterised as neither a material influence nor a successive modification of a medium, but a state or quality which the medium acquired. The claim that it moves in straight lines appears in "Problemata", see page 84. "I have chosen to define rays and refractions in such general terms as may agree to light in both cases." Newton 1717, 1952: 379.

84 other", "reflected or turned back onto the same medium from any other medium upon whose surface they fall","6 etc., using the only language which is at hand. We discuss this in connection with ontological metaphors as it illustrates well the role which the ontological metaphor plays as a prerequisite for theoretical reflection. The process metaphor of light moving depends on a prior ontological metaphor - substantivisation of light. We are far from arguing that "light" itself is a metaphorical concept; it is literal to the extent that it refers to a sensory stimulus, experienced in various sorts of situations, such as perception of sources of light (lamps, fires) and of things lighted; the differences between visible and invisible; dark and bright. The notion of light, however, becomes a metaphorical - hypostatised - concept as soon as moving becomes predicated of it in situations which do not include any experience of movement (i.e. to the exclusion of situations in which a source of light or the boundary of a lighted area are seen to move, in quite literal sense). The concept of light travelling, or being propagated, out of a luminous object into the surrounding space where it may be caught on its way through surfaces of physical objects and finally detected by the sense of vision upon entering the eye of an observer is a constitutive metaphor of optics: we do not dispose of any other scheme of thought allowing us to reason about light phenomena, and the physical models of light pursue the aim of explaining the mechanism of light displacement through the intervening space, the notion of movement being presupposed in them. That the seemingly self-evident concept of light travelling may be regarded as an act of a metaphorical extension from what is actually experienced to an interpretation containing an explanatory element not actually contained in the observed data, but borrowed from another domain of experience, has been pointed out by Toulmin (1953, 1967) and Bridgman (1927, 1960). Toulmin speaks in this context of the concept of "light as a substance in motion" as being a model rather than a metaphor. For him "suggestiveness and systematic deployability" are properties characterising models and differentiating them from metaphors, which are figures of speech not reflecting the nature of reality in a way in which models do - a model "suggests further questions, taking us beyond the phenomena from which we began, and tempts us to formulate hypotheses which turn out to be experimentally fertile.""7 We tend to treat as models such constructs which attribute more specified structure to their objects, and call the concept of light travelling a metaphor underlying such models. The concept of light travelling does not specify the way in which the travelling, or propagation, is taking place. It is rather the way of viewing light phenomena which makes possible the working out of different models, such as geometrical optics dealing with the laws of refraction and reflection etc. but is not interested in the physical mechanism behind them; the models of kinematic optics such as the emission model, treating light as a propagation of a substance; the aether wave model, treating it as a propagation of a disturbance in a material medium; and the contemporary concept of an immaterial field travelling through empty space. According to Toulmin (1953, 1967), the concept of light travelling came about as part and parcel of the discovery that it travels in straight lines, which, due to the habit of thought, seems common sense to us. The realisation that there is a metaphorical element involved in the step leading from the experience to the formulation of the principle of the rectilinear pro116 117

ibid. Toulmin 1963, 1970: 38.

85

pagation of light requires taking note of the fact that the actual experience of light phenomena is the experience of the geometrical configurations of shadows and things lighted, and does not itself include any sensation of what our language refers to as movement. The concept of light travelling from its source (a luminous object) to a sink, such as a mirror or the eye of an observer, enables us to think about optical phenomena in terms assimilated to ordinary mechanical experience and thus more easily reasoned about. Bridgman (1960: 150) claims: To realize that invention has been active here, we must think ourselves back into that naive frame of mind in which experience is given directly in terms of sensation. The most elementary examination ... shows that we never experience light itself, but our experience deals only with things lighted.

The concept of the rectilinear beam of light is "no more than a description of the geometrical relation between lighted objects".118 As indicated before, however, this description has been given in terms of movement since antiquity. Hooke (1680, 1969: 81) knows that Epicureans, Stoics, Peripatetics "all supposed it /light/ to pass in straight Lines", and Aristotle (Problemata XI.49, 904b.) explains: Why is it that light will not pass through anything thick, although it is less substantial and travels further and more quickly, but that sound will pass through? It is because light travels in a straight line ...

According to Bridgman (1960: 152-153), this interpretation involves an invented element because we have no possibility of verifying the assumption that there is anything present between the source and the instrument of measurement (e.g. an eye): The question ... is whether we shall regard it as a mere invention, made for convenience in thinking, or... ascribe a physical reality to it, that is, shall we think of light as capable of independent physical existence in the space between the matter that constitutes the source and the mirror? Now in spite of the resemblances pointed out ... there is at least one universal and fundamental difference between a thing that travels and light. We have independent physical evidence of the continued existence of the ball, for example, at all intermediate points of space; we can see it, or hear it, or feel the wind in the air as it passes, or even touch it. All these phenomena are independent of the initial and terminal phenomena, and hence ... we are justified in ascribing physical reality to the ball in transit. But with the beam of light it is entirely different; the only way by which we can obtain physical evidence of the intermediate existence of the beam is by interposing some sort of a screen, and this act destroys just the part of the beam whose existence we have thereby detected. There is no physical phenomenon whatever by which light may be detected apart from the phenomena of source and sink; that is, no phenomenon exists independent of the phenomenon which led us to the invention of a thing travelling. Hence ... it is meaningless or trivial to ascribe physical reality to light in intermediate space, and light as a thing travelling must be recognised to be a pure invention.

Bridgman, then, considers phenomena which appear to justify the literal treatment of light as a thing that travels: for example, the assumed transfer of energy through the intervening space, which he considers as inconclusive because there is no basis for asserting that energy is localised in space at all - energy is not a physical thing, but a property of a system as a whole; that is why it is pointless to ask where the energy is in the time interval between the emission and absorption of light. We might say that asking a question about the localisation

18

Bridgman 1960: 150.

86

of energy is a case of taking another ontological metaphor literally: the concept of energy, manipulating it conceptually as a kind of substance. Several other arguments for assuming that something actually proceeds, or changes, in the empty space between the source of emission and the sink in the time between emission and absorption are held by Bridgman to be inconclusive. Among these arguments for the literal treatment of light as something (not necessarily a substance) travelling in space, the finite velocity of light seems to be the strongest. It was, however, not before Roemer's astronomical observations made in 1676 that the finite velocity of light became an acknowledged fact. Before this, "instantaneous propagation" was attributed to light by the Cartesians and considered to be possible by others (Galileo). Although instantaneous propagation is no longer a part of the physical theory of light, the consideration of how this assumption was handled in its time may serve here as an illustration of the "as if" aspect of constructing scientific explanations. The assumption of instantaneous propagation means that the question "how fast?", which can be asked about things moving, was considered as inapplicable in this case."9 According to Descartes (La dioptrique, 1637), light is propagated not by the actual motion, but through an "endeavour" or "inclination" to movement; in "Principia philosophiae" (1644) he describes the mode in which light is propagated as centrifugal pressing or endeavour of the aetheral particles to recede from the centre of rotation of their vortex, and this endeavour conforms to the same laws as actual motion. Having explained the propagation of light as an inclination to movement, a kind of pressure rather than real motion, Descartes analyses the former in terms of the latter: he manipulates conceptually the "inclination to movement" in terms proper to real motion. In his analysis of refraction he resolves the incident and refracted rays into components (normal and parallel to the refracting surface), which is clearly a componential analysis of velocity (the distance travelled in a certain time). The same treatment of light phenomena: simultaneously assuming that light spreads out in an instant and explaining refraction with the help of derivations involving (finite) velocity is to be found in Hobbes.120 Both Descartes and Hobbes introduce in their geometrical derivations an element analogical to velocity, treating light as if it propagated in time (had a finite velocity), although the notion of the time of propagation is assumed not to apply to it. The manner of speaking of light in terms of movement common since antiquity, seems to have made it natural to treat it mathematically in these terms in spite of the assumed difference, without any need for theoretical justification. This approach is common to Hobbes and Descartes although both subscribe to different theories concerning the physical mechanism of propagation of light (Hobbes' "Tractatus" represents an early stage of the undulation theory). The movement metaphor allows us to explain optical phenomena in general kinematic terms independently of the consideration of physical mechanism. The property of instantaneous propagation was cast away in the course of the development of knowledge about the optical phenomena, which gave back much of the literalness to the notion of travelling as applied to light. With respect to this fact, Bridgman points out that it 119

120

Of course, this question could be and was actually asked about light, the answer being "in no time"; we are free to ask any question about anything, but the point in calling a question not applicable is that some answers negate a presupposition contained in the question, and this seems to be the case here. Tractatus opticus, 1644. Cf. Shapiro 1973 and Shapiro 1974.

87 is possible to re-structure the mathematical description of light phenomena in such a way that light is attributed an infinite velocity, through the change in the method of adjusting the clocks set at two distant places, contrary to the choice made by Einstein in relativity; this would not contradict the fact that light needs time to "go and come" (after reflection at a distant mirror) to the same point at which the emission took place because we could resign from the simplicity of the relation between velocity and "come and go time" introducing a different picture involving a significant difference between a process proceeding in one direction only and a process involving a reversal of direction. Interestingly, Bridgman speaks here of "reversing the direction of motion",121 using the same concept, or metaphor, against which his whole argument is aimed: that of a thing moving in space between the source and sink; it seems impossible to eliminate the concept of movement from the picture. Bridgman stresses further that the choice made by relativity to attribute a finite velocity to light was based on the simplicity of the image of ourselves as an observer from outside, watching a thing that we call light travelling back and forth like any physical thing .. .'22 (Indeed, such was the picture which helped work out the very principle of the relativity theory - Einstein is reported to have been initially inspired by an image of himself travelling on a beam of light, cf. Dreistadt 1968). In spite of difficulties with wording his counterargument in terms avoiding the notion of light as a form of movement ("reversing the direction of motion"), Bridgman is definite on the point: Physically it is the essence of light that it is not a thing that travels ... Of course the whole problem of the nature of light is now giving the most acute difficulty. The thing-travelling point of view, even as treated by Einstein, does not land us in a situation which is at all satisfying logically. We are familiar with only two kinds ofthing travelling, a disturbance in a medium, and a ballistic projectile. But light is not a disturbance in a medium, for otherwise we should find a different velocity when we move with respect to the medium ... neither is light like a projectile, because the velocity of light with respect to the observer is independent from the velocity of the source ... The properties of light remain incongruous and inconsistent when we try to think of them in terms of material things. Einstein's restricted relativity has made a great contribution in so grouping and coordinating the phenomena that they can all be embraced in a simple mathematical formula, but he does not seem to have presented them in such a light that they are simple or easy to grasp physically. The explanatory aspect is completely absent from Einstein's work.123 Bridgman is not only pointing out that the concept of light travelling is a construct helping to manipulate it conceptually and mathematically, but also criticising it as an inadequate explanation of physical reality. This is the position of a realist requiring of the physical theory or model to "come closer to physical reality".124 From this point of view, the rendering of light as travelling is not so much a helpful device whose "invented" character does not interfere with the services it renders, making possible the representation of physical facts; rather, it is a concept that falsifies the physical reality, preventing us from the correct insight.

121

122 123 124

'The asymmetry which results from reversing the direction of motion we may visualise as a sort of curvature in space and time, as of a small piece of an arc of a circle bent back on itself, with the two ends diverging." Bridgman 1960: 163. ibid. ibid.: 164-165. ibid.: 165.

88 Toulmin (1953, 1967) considers the metaphor of light as a thing travelling from a rather different position: he pursues its merits at the service of geometrical optics which it made possible, and he is not interested in questioning its literalness on the ground of physical arguments. Instead, he takes it for granted that we are dealing with the metaphorical extension of the notion of travelling as well as light, a "way of speaking" and not a representation aiming at as close a correspondence as possible to reality, whatever that may mean. While Bridgman is attacking the metaphor of light travelling as suggesting wrong physical ideas, Toulmin (1967: 19) takes the concept "light travels" contained as a presupposition in the optical discovery that it travels in straight lines, as the discovery that one can speak ... profitably of something as travelling in these circumstances, and find a use for inferences and questions suggested by this way of talking about optical phenomena the very idea that one should talk about anything as travelling in these circumstances being the real novelty. This "novel" way of seeing phenomena such as shadows and lighted areas enables us to ask new questions about the postulated agent - "questions like 'where from?', 'where to?' and 'how fast?', which are intelligible only if one thinks of the phenomena in this new way".125 The notion of light travelling constitutes an extension rather than a simple application of the notion of travelling: The introduction of the notion of 'light' as something 'travelling' is not the simple, literal discovery of something moving, like the detection of frogs in a flower-bed ... rather it is an extension of the notion of travelling to do a new job in the service of physics.126 The discovery that light travels in straight lines constituted a novel method of drawing inferences, e.g. about the lengths of shadows or the height of shadow-casting objects, with the help of diagrams of geometrical optics which represent light as filling or covering the space between the source and the lighted area, limited by the lines representing the boundaries created by opaque obstacles which "cut off" a certain part of the light falling upon surfaces behind them. Only the presupposition of light covering on its way the space between the "source" and the "sink" allows us to make sense of such diagrams, in contrast, for example, with the ancient concept of the eye being a source of a sort of antenna which stretches out and seizes the properties of the object it surveys. This way of representing optical phenomena is also the source of the notion of the light ray: light does not come in atomised rays; the concept of a ray results from the technique of reading straight lines of our optical diagrams into the phenomena.127 Most significantly, the idea of light "travelling", or "being propagated" the exact wording is of secondary importance128 - is prerequisite to the formulation of the laws of reflection, refraction and diffusion of light. This is why we call this kind of metaphor constitutive — it comes as part and parcel of the recognised regularities in nature and presents a novel method of drawing inferences which could not be conceived of in a different conceptual frame. 125 126 127

128

Toulmin 1967: 20. ibid. The notion of a light ray as the direction of propagation, i.e. the normal to the wave front, could only come to existence after the formulation of the wave theory of light by Hooke and Huygens in the second half of the 17th century. "Whether we speak of light travelling or as being propagated is hardly important, for either is an equally good interpretation of the geometrical picture - at this stage, only as much of each notion matters as is common to both." Toulmin 1967: 27.

89

4.2. Spatial metaphor 4.2.1. A general outline of spatial metaphor 4.2.1.1. The concept Spatial metaphor is the conceptual transfer of spatial relations upon non-spatial concepts, accompanied by the transfer of corresponding linguistic expressions. It is one of the basic tools which help structure our experiences, that is, make them capable of being reasoned and talked about. The basis of the transfer is provided by the experience: spatial metaphors "arise from the fact that we have bodies of the sort we have and that they function as they do in our physical environment".12' Which spatial relations are used for structuring which other kinds of experience is culture-dependent; the metaphorical feature transfer does not follow necessarily from the "givens" of experience. Metaphorical expressions allow alternative conceptualisations (the "deeply hidden" metaphors hardly allow them, and can only appear to us as metaphors when the possibility of an alternative conceptualisation becomes realised). However, spatial metaphors are not randomly assigned, but serve as a vehicle for understanding a concept by virtue of their experiential basis. Spatial metaphors are underlying conceptual metaphors, that is, they are not expressed directly in language, but serve as the basis for generating linguistic expressions (satellite metaphors). 4.2.1.2. Container metaphor The container metaphor is a kind of ontological metaphor which transfers to states, actions, activities, and events the structure of bound physical spaces. It is an ontological metaphor because it makes them into kinds of objects. We choose to classify it also as a spatial metaphor because the most important conceptual property of these objects is their spatial organisation, having an inside and an outside and a boundary between them. Lakoff and Johnson (1980: 16) argue that the container metaphor arises out of the fact that we are physical beings, bounded and set off from the rest of the world by the surface of our skins, and we experience the rest of the world as outside us. Each of us is a container, with a bounding surface and in-out orientation.150

This orientation becomes projected upon abstract entities. Various kinds of emotions as well as relationships, for example, may be conceptualised as containers: He is in love. He fell into a depression. He broke out of this marriage.

[29

Lakoff and Johnson 1980: 14. "° ibid.: 29.

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4.2.1.3. Motion and change It follows from what we said above that the container metaphor works in thought and language in connection with the conceptualisation of change in terms of movement. Consider further examples of expressions where motion functions as a metaphor for a change: The whole country is marching towards a state of chaos. We managed to set things in motion, which led eventually to the abolition of the old system. The way from the old system to democracy was long and painstaking. Analysing expressions such as these allows us to conclude that we conceptualise changes in terms of an underlying metaphor of which they are satellite linguistic manifestations. The conceptual affinity between dislocation and other kinds of change is also shown by their being classified as subclasses of the same superordinate category in the antique philosophy. For Aristotle and for Galen, for example, the qualitative change and change of position are cases of motion (κινητισ): If the categories are divided by substance, quality, place, action, passion, relation, quantity, there must needs be three motions: of quality, quantity and of place ..."' Of motion, there are six species: generation, corruption, increase, diminution, alteration, and change of place.132 If a body undergoes no change from its existing state, it is at rest; otherwise it undergoes motion.133 For Galen, motion includes qualitative motion (or alternation) constituded by changes with respect to colour, flavour, etc., and transference - change of position. 4.2.1.4. Orientational metaphor The term 'Orientational metaphor" was introduced by Lakoff and Johnson (1980) to name the transfer of Orientational terms up-down, front-back, in-out, on-off, deep-shallow, centralperipheral onto non-spatial concepts. The basis of this transfer is provided by the experience: the Orientational metaphors "arise from the fact that we have bodies of the sort we have and that they function as they do in our physical environment... Orientational metaphors give a concept a spatial orientation; for example, HAPPY IS UP"."4 Lakoff and Johnson suggest that most of our fundamental concepts are organised in terms of one or more Orientational metaphors. In some cases this spatialisation is such an essential part of a concept that it is difficult to imagine any alternative way to structure a concept:

131

132 133 134

Aristotle: Metaphysics 10.12. 1068a8-9.

Aristotle: Categories 14. 15al4. Galen 1979: 5. Lakoff and Johnson 1980: 14.

91 So-called purely intellectual concepts, e.g., the concepts in a scientific theory, are often - perhaps always - based on metaphors that have a physical and/or cultural basis. The high in 'high-energy particles' is based on 'more is up' '"

Writing on acoustics, Fonagy (1963: 49-50) expresses a similar idea about the sensomotoric origins of spatial terms being used in non-spatial contexts when he argues, for example, that "high" and "low" used to describe sound qualities are to be explained aus der Körperhaltung beim Singen von hohen und tiefen Tönen, wo gewöhnlich der Hals (oft der ganze Körper) gestreckt resp. zusammengezogen wird.

He observes that this metaphor was foreign to the ancient Greek writers on harmony. This means that experience does not determine the choice of particular spatial metaphors, which vary from language to language. A basic orientational metaphor is neatly summed up in the "more is up" formula, an "invisible" underlying structure organiser giving rise to expressions such as The temperature is rising. He is a highly sensitive person. Above all other things, I like exploring caves. Physical basis: If you add more of a substance or of physical objects to a container or pile, the level goes up. "* The "more is up" metaphor, like all ubiquitous underlying metaphors, is invisible largely owing to its non-paraphrasability - "high pressure" and "the rise in temperature" are just the "right" expressions to talk of the phenomena they refer to, without available alternatives; this is what produces the consciousness of speaking literally, i.e., non-metaphorically. Lakoff and Johnson choose to speak of "more is up" as a metaphor because it is their objective to expose the sensory basis of the process in which language and conceptualisation are formed, and of an "underlying" rather than a "dead" metaphor because it manifests itself in language indirectly through its satellite metaphors and retains its productive potential. Other orientational metaphors listed by Lakoff and Johnson are for example: high status is up control is up

health is up happiness is up

better is up virtue is up

The authors observe that There is an overall systemacity among the various spatialisation metaphors, which defines coherence among them. Thus, GOOD IS UP gives an UP orientation to general well-being, and this spatial orientation is coherent with spatial cases like HAPPY IS UP, ALIVE IS UP, CONTROL IS UP. STATUS IS UP is coherent with CONTROL IS UP.1"

'" ibid.: 8-9. 116 Lakoff and Johnson 1980: 16. 157 ibid.: 18.

92

4.2.2. Spatial metaphors in physics: where to find them The contributions of orientational and other spatial metaphors to the physical discourse occur on diverse functional levels (instances are given in brackets): • theory and concept formation, including - formation of abstract physical concepts (absolute time), - constructing scientific models (band theory of solids), - postulating particular scientific hypotheses (heliocentric cosmology); • explication of physical concepts for educational purposes (material models of space-time curvature); • rhetoric (style): re-wording of an independently formulable hypothesis for stylistic purposes (the arrow of time); • vocabulary including physical terminology and non-terminological parts of the lexis of physical texts. In this chapter we shall deal with the contribution of spatial metaphors to meta-theory, physical theory and concept formation. Its functions pertaining to other levels of physical discourse will be dealt with separately. 4.2.3. The metaphor of centrality and the Copernican revolution 4.2.3.1. The metaphor of centrality and its perceptual basis The words "central", "centre", as well as "peripheral", "periphery", are used in English with two metaphorically related meanings, the primary reference being to the geometrical configuration of physical objects. This spatial relation constitutes the donor domain from which the notion of centrality is transferred upon the non-physical order of significance. This transfer of meaning follows from our psycho-physiological make-up: if we focus our attention upon a visual object (granting it, for the given moment, priority among all the objects perceived), it occupies the centre of our field of vision. The metaphor provides conceptual and verbal formulation for the order of significance alternative to its rendering in terms of two other spatial metaphors, expressing the comparison by placing the things compared on a horizontal or vertical line, so that the more significant is "up" in the vertical and "forward" in the horizontal ordering. The other two spatial metaphors are more general as the orderings in terms up/down and front/back apply in comparisons with respect to numerous attributes. The two basic metaphors transferring the "UP/DOWN" orientation upon non-spatial concepts are "MORE IS UP" and "BETTER IS UP". The metaphorical association of "better" and "up" subsumes numerous evaluative attributes, such as "VIRTUE IS UP", "CONTROL IS UP", etc., and also "IMPORTANT IS UP"; thus, importance is hierarchically (vertically) oriented. Similarly, the metaphorical relation "BETTER IS FORWARD" is applicable to ordering things in view of numerous attributes, generally of all attributes which are inherently evaluative: e.g. a person is ahead of the others in view of achievements, intelligence, power, etc. (Another orientational metaphor in Indo-European languages, ordering things with respect to their goodness, mainly with reference to their moral, ethical evaluation, is the ordering left versus right, secondarily transferred to politics where it carries a more complex meaning.)

93 The metaphor of centre and periphery, on the other hand, is restricted in its recipient domain to the comparison of related objects only in view of their relative significance and attributes closely related to it in a given context, that is, such attributes which motivate the judgement of significance. Apart from imposing a "ranking order" upon a set of objects, the metaphor of centre and periphery seems to convey to some degree the idea of their relatedness, causal relationships included. In some contexts, the conceptual relation centreperiphery is, in addition to and in accordance with "more important - less important", that of the controlling and the controlled. 4.2.3.2. The central Sun and the metaphor The issue of the relation between the spatial metaphor of centrality and what is customarily called "the Copemican revolution" contains two assumptions, concerning its causes and the effects, respectively: - the assumption that the Copernican shift has resulted in the abandonment of anthropoteleological explanations in science; - the assumption that the metaphor of centrality contributed to the abandonment of Ptolemaism in favour of the new heliostatic and heliocentric theory. The former often appears in human sciences,138 occasionally also in an eminent contemporary physicist's commentary about his discipline (cf. Born 1964: 8-9). According to this view, the decentralising of the Earth in the Universe meant the (metaphorical) "decentralising" of man as its inhabitant in the picture of the physical world and, consequently, the relegation of the anthropocentric perspective from the scientific world view. That in Copernicus' time geocentricism and anthropocentrism were welded together is a popular misconception which originated in the humanities (Nietzsche, Freud), projecting the literal treatment of the metaphor of centrality onto the early reception history of the Copernican idea. That the shifting of the earth away from the centre and making it move was not regarded as debasing the earth and man in the period in question139 (in fact, it was interpreted as ennobling them) has been demonstrated by authors such as Blumenberg (1960), Koyre (1957, 1969), and Klein (1986), so we will not deal with this issue here. Whereas the former concerned the meta-theoretical consequences of the Copernican shift, the other issue refers to its origins. In what follows we will examine the question of the contribution which the metaphor made to the emergence of Copernican theory, commenting on a misconception (attributing the literal treatment of the metaphor of centrality to the Renaissance man) involved in Burtt's (1924, 1967) argument, and then arguing in favour of other ways to relate Copernicanism and the centrality metaphor.

Cf., for example, Freud 1970: 283; Nietzsche 1965a: 983; Russell, quoted in Cohen 1985: 243; Flew 1971: 88, quoted in Cohen 1985: 240; Zukav 1979: 114; Kesting 1986, 66-71: 66; Freudenfeld 1981:875. The earliest interpretation of geocentricism as the ennobling of man and Copernicanism as man's

debasement acknowledged by secondary sources on the subject is to be found in Fontenelle's "Entretiens sur la Pluralite des Mondes" from 1686, cf. Blumenberg 1960.

94 Burtt (1924, 1967: 28) comments upon the factors which made a favourable reception of Copernican theory possible in spite of the fact that the generally accepted geocentric theory gave an equally satisfactory account of the known facts of astronomy and was coherent with all the fundamentals of philosophical knowledge of the time: No one whatsoever could be expected even to entertain such a notion a hundred years prior to Copernicus ... But certain things happened during these hundred years that made it not quite so impossible to persuade people who could appreciate the advantages of a new point of reference to give it some scope in their minds. The Renaissance had happened, namely the shifting of man's centre of interest in literature from the present to the golden age of antiquity. The Commercial Revolution had begun, with its long voyages and exciting discoveries of previously unknown continents and unstudied civilisations; the business leaders of Europe and the champions of colonialism were turning their attention from petty local fairs to the great untapped centres of trade in Asia and America ... The Earth was circumnavigated ... The antipodes were found to be quite inhabited. It seemed a possible corollary that the centre of importance was perhaps not even in Europe. Further, the unprecedented religious upheaval of the times had contributed powerfully to loosen men's thinking. Rome had been taken for granted as the religious centre of the world for well over a thousand years; now there appeared a number of distinct centres of religious life besides Rome. The rise of vernacular literatures and the appearance of distinctly national tendencies in art added their bit to the same unsettlement; there was a renouncement, in all these respects, of man's former centres of interest and fixation on something new. In this ferment of strange radical ideas ... it was not so difficult for Copernicus to consider seriously for himself and suggest persuasively to others that a still greater shift than any of these must now be made, a shift of the centre of reference in astronomy from the earth to the sun. (emphasis HP)

This quotations demonstrates that the author regards the metaphor relating the spatial configuration of objects (central versus peripheral) with their relative status of importance as a factor in the development of physical thought. This assumption is implicit: Burtt does not thematicise the metaphor itself; rather, he treats it as an objective given of thought (just as the authors believing in the de-humanising of science by Copernicus did). His line of reasoning indicates that he is caught in the literal treatment of the metaphor of centrality. He makes no distinction between the metaphorical (in the last sentence) and spatial (in the preceding text) senses of centrality, and the whole argument is based on the assumption that the socio-political and intellectual changes to which he refers were actually conceptualised in terms of shifts between former "centres" and "peripheries". By means of this, a conceptual link is easily drawn between them and Copernicus' new hypothesis about the physical configuration of celestial bodies. Burtt seems to claim more than merely that the Renaissance climate of thought, in which all previous opinions taken for granted became invalidated by new developments and discoveries, facilitated the emergence of new and revolutionary theories in other fields, too, including astronomy. He describes the changes in terms of the "renouncement ... of man's former centres", which amounts to (unconsciously) suggesting that the metaphor actually structured the conceptualisation of these developments and that its literal reading - the lack of discrimination between the physical, spatial sense of centrality and its transferred sense - was a factor in the emergence of the theory shifting the physical centre of the universe away from the position it occupied before. (We call the suggestion unconscious rather than implicit because Burtt does not reflect at any point upon the metaphorical character of the association between spatial centrality and non-spatial "centrality", so that we may assume that the distinction did not present itself to him.)

95 In what follows we wish to argue that the metaphor of centrality played a role in the positive reception of Copernican theory, but not even approximately as simply and directly as assumed by Burtt. We shall assume that the physico-methodological considerations which made the central sun a preferable option (punctum aequans) were additionally supported by non-physical factors playing an auxiliary role, such as the cognitive need to bring the metaphysical map of the Universe, structured in spatial terms by means of the metaphor of centrality, into agreement with its physical map. In other words, we assume that at the outset of Renaissance there was a tension between the metaphorical centrality of the sun and the physical centrality of the earth in the universe. Hutchinson (1987) showed that among the mystical interpretations of the universe, the political analogy of the state, in which its component parts received political counterparts, might have played, via the metaphor of centrality, an important role in enhancing the acceptability of the Copernican rearrangement. The medieval political analogy binding the state and cosmology contributed to disturbing the correspondence between the material and the mystic geometry of the universe as the idea of the centralistic state started winning the upper hand over the concept of the indirect rule of the monarch via the nobility. The physically exceptional role of the sun in the planetary system (the biggest body, the source of light and warmth) led to its identification with the monarch,140 and the centralistic tendencies in the political thought demanded centralising the monarch in the spatial conceptualisation of the state. Following Hutchinson's argument, we assume that the peripheral position of the sun in the picture of the physical universe contrasted with its status in the metaphorically structured hierarchy of importance, and that Copernicus' theory "literalised" the metaphorical "centrality" of the sun. Although the medieval cosmology, with the earth in the centre, was in accordance with the other spatial metaphor, structuring the metaphysical universe in terms of low and high, so that the sun was higher than the earth, it did not agree with the metaphor of centrality which was commonplace in language and supplied the alternative principle of mystic geometry. The two metaphors: the metaphorical meanings of "central" and "low" are at first glance incompatible with each other, which occasionally led to such linguistic "paradoxes" as Wilkins's (1636: 68) statement that "the centre ... is the worst place". The iconography of the time illustrates the tension between the two coexistent spatialisation metaphors applied to the structure of the mystic universe and the attempts to resolve it. On Domenico de Michalino's fresco from the cathedral in Florence, the universe consists of concentric spheres of decreasing diameters placed upon each other, so that the highest is at the same time the central one."" We interpret this image as an example of an attempt to visualise the world in a way concurrently compatible with both spatial conceptualisations. The Copernican revolution did not resolve this tension because it was interpreted on the one hand as granting the due eminent (central) position to the sun, but on the other as recognising the splendour of the earth through "lifting" it into heaven rather than decentralising. The two contrary spatial metaphors tended to be applied alternately, depending on whether the sun or the earth was the focus of attention: whereas the metaphor of "low" 140

141

This identification of the monarch with the sun was questioned in the context of the papal and royal rivalry for power; Pope Innocent III, for example, claims that the sun is the counterpart of the pope, and the king is properly assigned to the moon; in both cases, the sun is the counterpart of the strongest authority. Hutchinson 1987: fig. 1.

96

and "high" guided the spatial conceptualisation of the earth's status, the metaphor expressing significance in terms of centrality was, of the two, applied only to the sun (before the accompanying philosophical frame was forgotten and the metaphor of the "central" versus "peripheral" earth re-invented in our time; see page 94). In some visual representations of the universe, the metaphor of centre versus periphery suppresses the vertical ordering: whereas in the normal Aristotelian hierarchy the earth is at the centre, when divine sovereignty was to be stressed, it was extremely common to represent the Aristotelian cosmos in inverted form with Heaven at the centre, and the Earth either absent, or at the periphery.142 Moreover, in such representations God and heaven are commonly represented by the image of the sun, so that they picture the world as heliocentric, and the correspondence between the mystic and the material geometry of the universe is broken. The virtue of the Copernican revolution was that, even if it did not resolve the tension between the vertical versus two-dimensional (spherical) arrangement of the order of value, it did resolve the other, more significant dissonance: that between the arrangement of astronomical objects in the metaphysical and literal spaces. It has frequently been argued that at the time Copernicus formulated his theory, the view of the moving earth and static sun was barely supported by scientific evidence, and therefore, some additional extra-scientific motivations have to be looked for as instruments by means of which the abandonment of the geostatic theory could be accomplished. Kepler's sun-idolatry has been devoted much attention; for him, the sun was intimately associated with deity, which made it appropriate that it occupied the central position in the universe. In fact, we find evidence for such an extra-scientific motivation already in Copernicus himself, in the fragment (1543, 1965, Book 1, Chpt. 10) stating: Then in the middle of all this stands the Sun. For who, in our most beautiful temple, could set this light in another and better place, than that from which it can at once illuminate the whole? Not unfittingly it is called by some the lamp of the world, by others the soul or the heir. Trismegistus calls it the visible God, Sophocles' Electra the all-seeing. And so the Sun guides as it were ruling on its kingly throne the family of planets circling around it. This fragment supports both assumptions which we made above: first, that the spatial metaphor of "centrality" played a part in the rise of the theory because it required the adjustment of the physical picture of the universe to the metaphysical picture it shaped; second, that the political analogy sun-monarch was a well-anchored part of the conceptual frame accompanying the emergence of the heliocentric cosmology, and contributed its own impulse to the latter. According to Hutchinson (1987: 95), it was ... the growing notion that society ought to be tightly organised around a central authority, instead of being loosely dominated by dispersed nobility, that made heliocentric astronomy succeed. In this view, the cosmological attitudes were supported by socio-political ones. The political symbolism attached to astronomy was taken seriously rather than as a mere figure of speech: detecting the correct symbolism was the problem of decoding divine instruction to mankind. 142

ibid.: 107. Hutchinson claims that "implicit in such a radical inversion of the physical order of the cosmos into its mystic order is the idea that the literal Aristotelian geometry gives too much prestige to the common man".

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The tripartite division of the cosmos into the fixed stars, the planets, and the earth received a political interpretation corresponding to royalty, nobility, and the commoners. The terrestrial sphere was the governed and the lowest one.143 The sun was frequently regarded as an analogen of the monarch: the solar image was adopted as a personal motif by rulers like Louix XIV, Richard II, the Visconti family. In view of this association, the Copernican system had different political implications than the Ptolemaic: they represent respectively the state with a strong central power and the decentralised state with strong nobility mediating between the king and "the common people". Hutchinson's study throws light upon the question of how the Middle Ages reconciled the following elements: the metaphor linking centrality to significance, the assumption that the sun was more splendid and significant than the earth, geocentric astronomy, and the tendency to literalise metaphors, displayed among others in enforcing isometry of the metaphorical and material arrangements of the objects in the world. Hutchinson claims that the Ptolemaic system was often quite consciously portrayed as a heliocentric system (!), in the sense that the sun was in the middle of the space between the earth and heaven, preceded by three planets and followed by a remaining three. In this way, medieval mystic cosmology attempted to find its way out from the metaphorical dilemma and to combine in one the low earth with the central sun. The sun was placed both in a prominent position: in the middle of the world, and higher than the earth, whereas the latter was the lowest (and at the world's centre, which was, however, suppressed in this representation). This was also the standard method of representing the king in his court - preceded and followed by three figures. The political implication of such an arrangement was to limit the power of the king by admitting an intermediary place for nobility: Although the Ptolemaic system placed the King at the centre of the ruling elite, it did not place him at the centre of the Universe.144

On the other hand, the central position of the earth was hardly interpreted as stressing the significance of the people; for the interpretation of their status the low/high metaphor seems to have been more apt. To sum up, two metaphors of a different kind interacted in the process leading to the enhancing of the acceptability of the heliocentric hypothesis: the spatial metaphor expressing importance and control in terms of centrality, and the metaphor relating the state and the universe. If Hutchinson's thesis is correct, the latter can be regarded as a clear-cut example of the interactivity of a metaphor; whereas the cosmos is initially examined as the source of information concerning how to arrange human affairs, the changing ideas about proper political forms eventually exert their own influence upon the image of the cosmos. The process in question consists of the interaction of such components as • the state with its component parts: monarch, aristocracy, common people, • the political theory, • the spatial metaphor of centre/periphery applicable to non-spatial systems, • the scientific model of the physical universe, spatially arranged, • the metaphor mapping the components of the state upon the components of astronomical universe, • a spatially arranged system resulting from the application of the spatial metaphor centre/ periphery to the system of the state, 143

ibid.: 103.

98 • a separate, mediating level of a "metaphysical Universe" as an analogen of the spatially arranged system of state. We speak of a "metaphysical Universe" as an analogen for the spatialised representation of the state distinct from the physical universe because a direct mapping between the Ptolemaic physical universe and the spatialised state is deficient, with the projection needing an intermediate term - a system of astronomical correspondences for the state which is spatially arranged like the state. It is through this intermediate level that intuitions about the structure of the physical universe became affected, ultimately contributing to the correction of the astronomical hypothesis. The tension resolved by the Copernican rearrangement of the physical universe can be represented schematically as follows: subject I metaphysical domain UP/DOWN metaphor subject 1: Universe subject 2: state Earth: low common people: low Sun: high monarch: high CENTRE/PERIPH. metaphor Sun: central monarch: central

subject II physical domain physical universe earth: low sun: high sun: peripheral (or "middle")

With this simplified treatment we do not wish to convey the idea that we regard these to be the sole factors in the extra-scientific motivation of Copernicanism. The conjoined effect of the two metaphors was certainly just one among numerous factors enhancing the acceptability of the new theory. How far other metaphors, symbolic representations, and mystical concepts contributed to this process, we do not aspire to examine in this work; in what follows only a brief hint will be given at the putative metaphorical aspect of the geodynamic (heliostatic) hypothesis. 4.2.3.3. The metaphorical aspect of geodynamic hypothesis On the fringes of the treatment of the contribution which the spatial status metaphor of centre and periphery made to the heliocentric idea, a remark enforces itself that there seems to have been another status metaphor in operation, which provided the extra-scientific support for the geodynamic aspect of the Copernican theory - the metaphor privileging the static versus the moving things. It is no spatial metaphor, but deserves being mentioned here as another status metaphor with experiential basis, coherent with the former. In "De revolutionibus" (1547, 1965, Book 1, Chpt. 8), Copernicus applies this evaluative approach to movement to support his thesis when he says, distorting Aristotle's original thought,145 that according to the common opinion the unmoved is more noble than the moved: In addition to this, the state of immobility is, according to the general view, more noble and divine than that of alteration and variability, for which reason the latter is more properly attributed to the Aristotle thought that variability implies corruptibility, but he did not apply this principle to circular movement; it is perfect as it has nothing contrary to itself.

99 Earth than to the whole world. And I add to this, that it is rather nonsensical to attribute motion to the supporting and the setting rather than to the supported and the set.

Blumenberg (1960) thinks that the origin of the evaluative approach of the Middle Ages to movement is to be sought in the Aristotelian concept of God as the unmoved mover, which places it in a philosophical rather than a metaphorical context. However, Aristotle does not always associate rest with dignity and high status. On the contrary, the fact that the earth rests proves its corruptibility, whereas the circular motion of the stars proves their perfection.146 Whereas the concept of the unmoved mover certainly contributed to the establishment of the conceptualisation of the unmoved as in a sense superior to the unmoved, the basis for this conceptualisation is of a more primary kind: it follows from human experience in a physical environment. Large static objects have probably always impressed man, rendering his causal powers meagre and evoking the associations of majesty and might. Conceiving large static objects as agents in the context of smaller moving ones is manifest, for example, in the way of speaking about magnetic effects: even for the ancients, it is the magnet which draws other small metallic bodies toward itself, whereas they are passive recipients merely apt to receive the attraction (cf. Roller and Roller 1954; Galen 1979: 73). In numerous social transactions, such as greetings, military parades, religious rituals, coronations, etc. the distinction moving/static functions symbolically as a status indicator. Thus, the heliostatic and the heliocentric aspects of the theory cohere with each other also on the metaphorical level, since the same evaluation is assigned to centrality on the one hand and immobility on the other through the respective status metaphors. 4.2.4. Spatialisation of time 4.2.4.1. Space and time in general language The way time is rendered in physical research is an offshoot of our everyday language which parallelises time and space, coupled with the tendency to render abstract notions and relations in a visual form. The tendency to speak of time in terms applicable to space is a common practice of language. Consider the following examples of English expressions, taken from everyday language and the language of physical theory, which do not distinguish between two kinds of ordering, the relation of juxtaposition in space and the relation of succession in time: • positional prepositions denoting positions of objects in space and "positions" of events "in" time: "in", "at", "on"; • relational prepositions denoting the sequential order of objects in space and events in time: "before", "after", "ahead", "behind", "in front", "in back", "between"; • directional prepositions "from", "up to", and "through" (as in "through Thursday", American English); • adjectives "long", "short", denoting spatial dimensions of objects and duration of processes in time; Aristotle maintained that corruptibility is an attribute of things only which contain contraries. The circular motion of the planets has no contrary to itself, so they must be perfect; the resting earth is not of that kind because, if removed from its place, the centre of the universe, it would come back to it through motion in straight line towards the centre, which has its contrary - motion in straight line away from the centre; hence, the earth contains contraries, and is corruptible.

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• adverbs "far", "near", denoting the distance of objects in space and the duration of time between events; • verbs such as "fill" and "occupy", denoting the relation between objects and their positions in space as well as events and their "position in" time; • substantives such as "position" and "occupancy", denoting the relation space - object and time - events, and "interval", denoting the spatial relations between objects and relations in time between events; • substantives such as "direction", "directionality", "(a)symmetry", referring to the sequential order of objects in space and events in time; • expressions referring to the change of the sequential order of objects in space and events in time, such as "inversion", "(irreversible", "reversibility". Two alternative approaches may be taken with respect to this fact: • All these words express abstract relations which manifest themselves independently in time and space and as such they have a meaning which is neutral with regard to the difference between time and space; none of the two fields of their application is to be treated as primary. • All these words are primarily spatial and become applied to time only secondarily, which amounts to a metaphorical spatialisation of time. The first of these two approaches is akin to the views of philosophers of such different backgrounds as Newton, Kant and Russell, for whom time and space are intrinsically analogous; if we accept this analogy as objectively given, the fact that in talking about them we use the same words appears to be its natural expression. Whichever of the two above-mentioned approaches we are inclined to accept, we must admit that the parallel linguistic treatment of time and spatial relations goes hand in hand with the spatialised mental representation of time of which Jones (1982: 79) says: The spatial approach is frequently used in the ... handling of time ... When we speak, for example, of time intervals and durations or of time order and sequence, we have in mind an imaginary long straight axis of time with points on it locating events and distances along it measuring the elapsed time between events. The very words interval, duration, sequence evoke spatial images that help us think about time and its measurement. In other words, for quantitative and related conceptual purposes, we picture time as a kind of one-dimensional continuous space. It is in this spirit that the theory of relativity treats time as the fourth dimension, added to our physical three-dimensional space. And one finds this spatial view of time throughout scientific literature. The fact that we form a spatial mental image of time to which Jones is referring in this comment does not in itself contradict the view that the concepts expressed by the linguistic expressions listed above are applied to time and space on the equal footing (without meaning transfer involved). However, we shall accept here the other view, strongly supported by cognitive semantics.147 We agree with Rigotti (1986: 157) that Time is ... expressed metaphorically ... It is ... one of the few [subjects] that can only be expressed in this way. It takes its properties, its qualifications and definitions ... exclusively from other contexts, the most important being spatial contexts.148 147 148

Cf, for example, Vanparys 1984; Radden 1981; Lakoff and Johnson 1980; Dirven 1983; Clark 1973. Bergson, quoted in Wheelwright 1968, articulates an original thought arguing that 'To conceptualize time ... is to spatialize it; for it is only thus that time can be divided into unites - whether these unites correspond to the markings on the face of a clock, or the notches of a sundial, or the amounts of sand or water passing through an apperture, or the diminished lenght of burning candles".

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In what follows we present such interconnected levels of the metaphorical redescription of time in spatial terms as • "time as a moving object" metaphor in its two aspects: - the Newtonian metaphor of the "flow of time" as the embodiment of the absolute theory of time, - the rendering of time as a point moving on a line in the direction from the past to the future; • static rendering of time as a kind of space or one of its dimensions: - the conceptual representation of time as a receptacle of events as the embodiment of the absolute theory of time, - the notion of time as the "fourth dimension" of space, - the spatial model of space-time in relativity and its "dynamic" misinterpretation, - the concept of space-time curvature based on the analogy with the geometrical curvature in three dimensions. 4.2.4.2. Time as movement: the experiential basis The expression "flow of time" expresses and stabilises the tendency ubiquitous in language: that of conceiving change as motion (see the beginning of this chapter). In English, among other languages, this conceptualisation provides for a spatialised concept of time structured in terms of movement in a specified direction. The fact that conceiving time in terms of motion is not an unavoidable result of human psychophysiological experience, but an option available to cultures and languages has been pointed out by Whorf (1956: 151) in his discussion of the culture and language of Hopi: To the Hopi ... time is not a motion but a 'getting later of everything that has ever been done ...'

Time in the sense of a "flowing" continuum does not appear in Hopi. Recognitions like this, of possible alternatives to our ways of conceptualising experience, make us attentive towards the metaphorical bias of our own concepts. The way in which English imposes orientation upon the distribution of events in time already suggests that its notion of time is shaped by a spatial metaphor based on human physiological make-up. The very choice of the direction front/back rather than any of the other possible directions (above vs. below, left vs. right), and of the particular items for describing relations in time (before, after, ahead, behind etc.) suggest that we are dealing with metaphorical transfer of spatial concepts based on the basic aspects of human perceptual and sensomotoric experience such as the canonical direction of movement and the direction of canonical encounter. In English, time and its segments are structured in terms of the "moving object" metaphor, with the future moving toward us, as in the expressions: The time has come when ... The time has long since gone when ... The time for action has arrived. Coming up in the weeks ahead ... I'm looking forward to the arrival of Christmas. Friday rushed by.

102 In the spatial metaphor articulated in these expressions, we are facing the oncoming future which turns into past as it passes by.149 Time appears here as a directed one-dimensional continuum in which the past is in the back of now and future in front of us. This orientation has an experiential basis: The experience of space as well as the experience of time is closely associated with the perception of changes in the field of vision, such as that experienced when we move relative to our environment. We can reconstruct the experiential basis for this transfer of meaning: moving through space, we change our field of vision and perceive different states of affairs. Similarly, the experience of time amounts to the experience of changes in the states of affairs in the perceived environment. In this metaphor, our movement with respect to the spatialised image of time is in the canonical direction of movement, forwards on the horizontal plane. This direction is selected to conceptualise and name the direction in which we "move" in time, with the past (things already seen) lying in the back and the future (things to be seen) in front of us, just as when we move through space. The canonical direction in which we move as human beings is forwards on the horizontal plane, and the "canonical encounter" of a human being with the elements of the environment towards which the attention is turned is by facing them. During the relative movement of the observer and the environment, the things to be perceived lie in front of us, the things already seen having passed behind. This leads towards conceiving time in terms of the past (things already seen) lying in the back, or behind, and the future (things to be seen) in front, or ahead of us. The front/back orientation immanent to us as human beings becomes transferred upon other moving objects which generally receive a front-back orientation, so that the front is in the direction of motion. Hence, time is facing us while moving in our direction. Due to the "face first" orientation being imposed upon time as a thing that moves, things which happen first lie before, or ahead of, things which happen next: Thursday comes before Friday. 4.2.4.3. Time flowing past, or the forward sliding present? Clark (1973) and Lakoff and Johnson (1980) point to an interesting property of our everyday metaphor for time conceived in terms of movement. In addition to time moving towards us, there is another way in which we conceptualise the passing of time, in which time is stationary and we move through it: As we go through the years ... We're approaching the end of the year.150 Lakoff and Johnson (1980: 43-44) argue that What we have here are the two subcases of TIME PASSES US; in one case, we are moving and time is standing still; in the other, time is moving and time is standing still. What is in common is relative motion with respect to us, with the future in front and the past behind. That is, they are two subcases of the same metaphor, as shown in the accompanying diagram. 149 150

Lakoff and Johnson 1980: 42. Lakoff and Johnson 1980: 43-44.

103

Time is a moving object and moves toward us

From our point of view time goes past us, from front to back Time is stationary and we move through it in the direction of the future".

This dual nature of the "time passes us" metaphor led Akhundov (1986: 96) to an overestimated interpretation of the difference in the representation of time in Christianity and in modern physics. Akhundov assumes that, in the passage from Christian conceptions to modern thermodynamics, time has reversed its course ... religion is turned toward a coming salvation and escape from time, so that the Christian river flows out of the future. It is in this sense that we must understand St. Augustine's thesis that the present is exhausted as it moves continuously from the future to the past. Actually, here the image of the river is no longer applicable, and we must instead use that of an hourglass ... The contours of this model resemble the light cone in the theory of relativity, but in modern physics the flow or 'arrow' of time has ... changed direction and returned to the ideal of antiquity from the past toward the future.

In fact, there is no necessity for the assumption that the direction of time flow became inverted. Rather, we are dealing here with the two alternative conceptualisations Lakoff and Johnson refer to: the observer (the present moment) moving forward on a line from the past towards the future versus the observer (the present) standing still and awaiting the oncoming future which turns into the past as soon as it has passed by. In the representations of time as an object moving upon a line - a point which has evolved into an "arrow" in the language of modern thermodynamics - what moves is not time as such in its totality, but the present, the moment of observation constituting the border between the events which have taken place and those which will take place. The linguistic analysis by Clark and by Lakoff and Johnson makes it redundant to assume that the river of time has changed its direction. The direction of the relative movement of the observer with respect to the past and the future remains the same in the Christian image of the river flowing out from the future, Newton's absolute time flowing in its even tenor, and the time arrow of contemporary thermodynamics. What has undergone change is the perspective from which mobility becomes attributed to the sequence of events connecting the past and the future in one case, and to the observer himself in the other. The first of these two perspectives is the one which produces the Newtonian metaphor of "time flowing in its even tenor", in which time is conceptualised as a continuum moving past the present moment (the observer). The second perspective, with an observer (the present moment) moving toward the future, underlies the way of speaking about time exemplified by the comment by Eddington (1968: 51): Events do not happen; they are just there and we come across them. 'The formality of taking place' is merely an indication that the observer has on his voyage of exploration passed into the absolute future of the event in question.

A generally-known implementation of this conceptualisation of time, identified with physical processes, is Eddington's "arrow of time". We postpone its presentation until the chapter on style and rhetoric because, notwithstanding the fact that it is based on the spatialised conceptualisation of time, we have classified it as a "figure of speech" - the means of expression rather than of conceptualisation, helpful in verbalising physical ideas

104 but not contributing any significant impulse of its own, either to the formation of physical theory and shaping its concepts or to meta-theoretical reflection. 4.2.4.4. "Flow of time" and the absolute theory of time Since it was established in antiquity, the image of a river as the metaphor for time has been commonplace in literature. Heraclit was probably one of the first philosophers who used the metaphor of the flow to describe the ubiquitous change of all existence ("panta chorei"). Plato in Cratylus attributes to him comparing reality to a river and saying that you cannot step twice into the same river.151 Restating Heraclitus' saying as the well-known "panta rhei" (everything flows), he established the image of a river as a metaphor for time for the subsequent twenty five centuries. Ovid (Metamorphoses, 15.178-181, 1985: 286) wrote: Everything streams by. Each image wanders as it takes shape. Years slip by in continuous motion like the flowing of a stream. For the stream cannot stop, nor can the flitting hour. For Marc Aurelius (1968,1: 69), There is a kind of river of things passing into being, and Time is a violent torrent. For no sooner is each seen, than it has been carried away, and another is being carried away by, and that, too, will be carried away.

Time is rheuma in Greek, and flumen in Latin, "a process of flowing, a thing that flows".152 Several centuries later, Bacon (1620, Aphorism 71, 1990: 152) wrote: Tempore (ut fluvio) leviora et magis inflata ad nos devehente, graviora et solida mergente.

Several properties make a river an appropriate carrier for the spatial conceptualisation of time which it both expresses and stabilises: • continuous change through movement: representing changes in terms of movement in space, the "river of time" metaphor expresses and stabilises the underlying metaphor of change as movement; • endlessness - both the endlessness of the flow of a river as a process and the endlessness of a river in the field of vision; • one-dimensionality: because of its shape, with its length dominating other dimensions, it is easily idealised as one-dimensional (a line); • horizontal orientation (time is horizontal in our language: we move forwards relative to time, that is, on the horizontal plane just as we usually move on the horizontal plane in space). In what follows we want to argue that the image of a river as the embodiment of the spatialised conceptualisation of time was not merely ornamental, but may be regarded as a factor psychologically supporting the theory of absolute time as represented by Barrow, Newton, and Gassendi, to name but a few of its seventeenth century adherents. Several centuries after Heraclit, the image of the flow of time appears in Newton's "Principia" (1725-6, 1952: 89) as the embodiment of the absolute theory of time presented in the following wording:

151

152

Cf. Ahl 1985: 286. ibid.

105 Absolute, True, and Mathematical Time, of it self, and from its own nature flows equably without regard to anything external, and by another name is called Duration: Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by the means of motion, which is commonly used instead of True time; such as an Hour, a Day, a Month, a Year. Newton's concept of absolute time comes from his tutor Isaac Barrow, who expresses his views in the following words: But does the time imply motion? Not at all, 1 reply, as far as its absolute, intrinsic nature is concerned; no more than rest; the quantity of time depends on neither essentially; whether things run or stand still ... time flows in its even tenor.1" Pierre Gassendi (1986: 104) also subscribes to the notion of absolute time: I, at least, know one single time, which, of course ... may be called or considered abstract, since it does not depend on things; for whether things exist or not, whether they are moving or in a state of rest, it always flows uniformly, subject to no changes whatever. We suggest that the metaphorical spatial conceptualisation of time expressed verbally with the phrase "flow of time" is intrinsically connected with the notion of absolute time in its two aspects: - uniformity through space, - independence from physical processes. The absolute theory of time differs in the second factor from the relational theory and in both from the contemporary relativistic rendering of time. Absolute time is uniform through space The representation of time as a flow of events along a one-dimensional continuum in the direction from the future towards the present and from the present into the past expresses and stabilises in a barely noticeable way a commonsensical assumption which had not been questioned before the advent of relativistic physics: the assumption of the existence of the absolute present, or, using the language of the relativistic physics, absolute simultaneity of distant events, meaning the independence of time from its position in space. There is one "river of time"; the metaphor spatialises time into a constantly moving line divided into the past and future section through the present moment. The present moment in this image is unrelated to any consideration of spatial dimensions, that is, independent from the localisation in space. Before the days of special relativity, it was quite acceptable to suppose that the entire universe had real existence for only one instant (now!), the past world having passed out of existence, the future world not yet come into being.154 The metaphor of the flow of time precludes any consideration of the differences of the spatial localisation of the observers. It represents the present (now) as the unique point from which, or at which, the observing is done, the unique zero-dimensional point of division between the past and the future: hence, so to speak by definition, the present must be the same for all observers. In this image, there is no place for the consideration of physical space. (One of its 153 154

Barrow 1860, 2: 160. Quoted in Capek 1966: 36. Davies, quoted in Ahl 1985: 275.

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dimensions is already occupied by time, and it can hardly be represented in the remaining two.) The resulting uniqueness and independence of the zero-dimensional "now" from spatial considerations (i.e. its identity for all observers) is an "underlying assumption" of prerelativist physics, which can only be recognised after an alternative point of view has been made available by the relativistic "fusion of time and space", eliminating the notion of the universal "now". Absolute time is independent from physical processes The notion of absolute time arose out of the conceptual representation of time as a moving object coupled with the conceptual emancipation of time from physical processes. Speaking of the conceptual development leading to the idea of the passage of time independent from physical becoming, Mach explains the conception of absolute time as the result of a psychological process in which time becomes abstracted from changes because we know that none of them is essential for measuring time. Since no process seems to be essential with respect to the measurement of time, we overgeneralise this recognition and conceive time as independent of any succession of changes. In other words, the recognition that the tempo of time flow does not depend on the tempo of any particular process leads to the conception in which it does not depend on any process at all (cf. Mach 1883, quoted in Smart 1964: 126). This conceptual emancipation of time from physical processes was supported by the development of many alternative techniques for measuring time, which led to the insight that the processes used in them were not essential for the passage of time itself.155 Fräser (1982: 13) comments upon the way in which the pursuit of technical progress in the measurement of time has been associated with the hidden assumption about the existence of an absolutely true and objective rate of its "passage" saying: The notion that a continually improving accuracy of clocks makes sense implies a particular view of time, hidden by convention. What is being claimed is that the improved device indicates more truly the rate at which time passes the prior devices did. Evidently, therefore, the rate at which time passes ... [can] only [be] recognised and recorded with increasingly greater precision.

4.2.4.5. The paradox of time flow The concept of absolute time involves a paradox which becomes identifiable if we make manifest the underlying metaphor using the simple method proposed i.a. by McCloskey (1964) for probing the metaphorical vs. literal character of linguistic expressions: asking questions which normally make sense if asked about a usual referent of the expression. Hinckfuss (1975: 63) exposes the nature of the paradox saying: 155

In the Middle Ages, many sorts of time measuring devices were known, each depending on a different kind of a cyclical process. The first clocks were gnomons which measured the movement of the celestial spheres, just as nocturnal dials and shadow clocks already known in early antiquity did. The mechanical clock, even if it was initially meant to simulate these movements, functioned in a way which was independent of them, like water, sand, and oil clocks. The ultimate conceptual divorce of "true time" from the actual movements of the celestial spheres is reflected in Copernicus' proposal for a calculus introducing corrections in time measurement obtained by the observation of heavenly bodies: he proposed to obtain a universal and precise measure of motion through calculating mean astronomical day, which does not correspond to the actual length of any individual day.

107 If time flows, it must be flowing at a certain rate. With which rate does the time flow? Now, the rates of flow are always with respect to time. So if time flows, it must be flowing with respect to itself. But nothing can flow with respect to itself. So time does not flow.

In a similar vein, Smart (1949: 485) speaks of the pseudo-question 'how fast am I advancing through time ?' or 'How fast did time flow yesterday?'

He continues: We do not know how we ought to set about answering it. What sort of measurements ought we to make? We do not even know the sort of units in which our answer should be expressed ... It is clear, then, that we cannot talk of time as a river, about the flow of time, of our advance through time, or of the irreversibility of time without being in great danger of falling into absurdity.

The point of these remarks is that the expression "time flows in its even tenor" must be classified as metaphorical because the image of the flow of time is a representation of time itself as a process in time. Newton's formulations "without relation to anything external" and "in its even tenor" are logically unsatisfactory: there is nothing which controls the rate of time's flow, so it is meaningless to say that it is or is not uniform. As we have seen, implicit in the notion of absolute time is its spatialised representation as a moving object, or a form of movement. Movement, however, involves two parameters space and time. This way, the metaphorical conceptualisation of time as a moving object introduces the time factor twice into the picture. The spatial image of time as a moving object is an indiscernible metaphor representing one variable in terms of another variable and itself. The same metaphorical bias occurs in conceptions which propose regarding time (literally) as the fourth dimension of space, and is responsible for the conceptual misrepresentation of space-time in some expositions of relativity; cf. page 111. 4.2.4.6. Time as a receptacle of events and the absolute theory of time Another conceptualisation of time which embodies the concept of absolute time is that of time as a receptacle of events, based on an analogy with space. Using an expression proposed by Capek (1956), in this conceptualisation time is represented as a container of physical changes, its supposed attributes being its existence prior to and independent from its changing contents. The container conception of time is grounded in the conceptual analogy manifesting itself in language in the use of such prepositions as "through" and "in" with respect to time as in "go through time" and "happen in time". This analogy has frequently been an object of philosophical reflection. In physics, it was displayed in the concept of absolute time. Time-receptacle and the analogy between time and space The assumption about time being analogous to space, frequently to be encountered in the works of classical physics, coupled with the belief that space is in its existence independent from its physical contents (matter), led to the analogous conceptualisation of time as an entity which exists independent of things happening in time. This assumption has been formulated clearly by Newton (1725-6, 1952: 10):

108 For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation.

Barrow (1933: 130) gave the spatial metaphor underlying this view its most explicit formulation: Time is in some sort the space of motion.

For Newton and all who subscribe to the theory of absolute time, time is in its own nature empty and only in an accessory and contingent way filled with changes. Changes are in time, not time itself. As late as the beginning of this century, Russell defends this view of time by speaking of two classes of entities - those which have positions and those which are positions, time belonging to the latter. The terms which have positions are related to the terms of the other class by the relation of being at the positions, or occupying the positions, the relation of "being in" or "at" being itself indefinable and fundamental. The physical contents of time are different from time itself, and the existence of time does not imply the existence of changes. Thus, for Russell as for Newton, time is analogous to space in being independent of the contents and the relation between their contents and time and space, respectively, is that of occupancy. Just as space is a container of all matter, so time is a receptacle for changes. In this spatialised image of time, time bears the same relation to events as space to matter. In the concept of absolute time, the assumption that space and time are analogous in their relation to matter and events, respectively, meets the concept of absolute space. The latter was based above all upon the consideration that the motion of a body can be measured relative to many other bodies alternately, which resulted in the conclusion that bodies and their very existence are indifferent to movement generally, so that the point of reference for movement must be empty space itself. The same relation became projected upon time and processes in time.156

It is to be noted that the assumption about there being an analogy between the relation time/events on the one hand and space/matter on other does not in itself amount to the theory of absolute time. It is only so insofar as space itself is conceived as absolute, that is, as a receptacle of matter prior to it and not influenced by its existence. The analogy between time and space co-occurs also with the relational view, in which space and time share the feature of being nothing in themselves, but only constituting the order of things. The rejection of the receptacle concept with respect to time usually co-occurs with the relational approach to space. For those, on the other hand, who assume space to be absolute, the insistence on the analogy results in the notion of absolute time. This is, for example, the case for Newton, who had to assume that space is absolute because of the axiom of acceleration being due to force; objects move with different accelerations relative to different systems, so if there were no absolute point of reference we would have to assume a different force acting upon a body in every case. As space is absolute and time is analogical to it, time must be absolute, too. This view of the relation between time and physical becoming was in no way generally accepted in the classical period. The alternative, relational view of time, rejecting the receptacle concept, is exemplified by Leibniz who says: "that ... inference would be right, if time was anything distinct from things existing in time ... But... instants, considered without things, are nothing at all; and ... they consist only in the successive order of things." (Leibniz's Third Paper, in Smart 1964: 90); "Time does only co-exist with creatures, and is only conceived by the order and quantity of their changes" (Leibniz's Fifth Paper, ibid.: 96).

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An excursion: remains of absolute time The general acceptance of the relational view of time in the present day does not eliminate the way of thinking shaped by the receptacle and moving object metaphors. Consider the following claim by Rigotti (1986: 159): These images ... rest on two fundamental equivocations, or at least on two non-verifiable premises. The first of these premises is that time moves; the second is that time and events are one single entity ... The first premise ... has already been exposed to stringent criticism ... The second premise is similarly widespread and equally unjustifiable: describing events as time, and not in time. This is probably the product of a way of thinking which is incapable of separating time from its contents, seeing it as a quantitative and phenomenological element instead of as an abstract and neutral parameter, (emphasis HP)

This is an exact reversal of the criticism by Capek (1956: 38), characterising the classical science as mistakenly assuming, with respect to time, the distinction between the receptacle and its contents: Just as space is a container of all matter, so time is a receptacle of all changes ... This was a basic dogma of classical science ... the distinction which under the double impact of Newton and Kant still dominates to a great extent our mode of thinking.

For Rigotti, it is the identification of time with events that is metaphorical (Rigotti associates its origins with the metaphor of the river for time in ancient writers). She calls time an "abstract parameter", but this parameter is conceived as a container whose contents are events. In Grim (1993: 64), both metaphorical spatialised conceptualisations of time - as a receptacle and as a moving object - become manifest. Grim speaks of "Geschwindigkeit der bewegten Objekten in der Zeit", producing an utter confusion with respect to the notion of velocity through the conceptual misrepresentation of time in terms of the receptacle metaphor in which things do move through, or in, time. The notion of movement - a process involving both time and space - becomes misapplied to time alone. At another point, Grun describes the concept of time dilation (itself a spatial metaphor - the word "dilation" refers originally to a change in spatial dimensions) in relativity as the assumption that, in two systems accelerated relative to each other, time moves with different velocities ("unterschiedlich schnell ablaufend").157 In this way of speaking, the rate at which events happen becomes again projected upon time, conceived as a moving object. 4.2.4.7. Time flow, time receptacle, eternity, and classical determination Time as a receptacle of changes and time as a moving object do not seem to be mutually exclusive conceptualisations; rather, they provide two complementary perspectives, or ways of speaking, existing side by side. According to Akhundov (1986: 60), they already co-occur in a philosophical formulation in Milesian philosophy, in which time is represented in two projections: A view of it from the temporal world yields the model of a dynamic time that flows from the past through the present and into the future, whereas viewing time from the extratemporal world results in a 'spacelike' model in which past, present, and future can be taken in a single glance... The world appears at once in its totality. Grun 1993: 52.

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In the latter conceptualisation, time becomes a receptacle of all that has ever existed, exists and will exist. Akhundov calls this second model "spacelike" because of its static character, with everything co-occurring simultaneously. This projection has religious connotations: the gods could see everything at once from their place in eternity. The concept of space-like eternity comprising at the same time (or, rather, outside time) the past, present, and future finds its continuation in Christian thought. The utterly independent, uniform flow of time takes place relative to the immobile background of timeless being: eternity, which is an attribute of God. When, as in Newton's "river of time", the conceptualisation of absolute time as a moving object is evoked, eternity may be regarded as implicitly present, constituting a background for this process: it is relative to it that the flow of time is taking place. On the other hand, whenever it is maintained that "eternity" as understood by medieval Scholasticism is basically identical with the "absolute time" of classical mechanics,158 the conceptualisation of absolute time evoked is that of a receptacle of events. The tendency to spatialise time in an image in which past and future coexisted in juxtaposition, consonant with the idea of predestination in religion, was realised in physics as classical determination: The God of St. Thomas and Calvin shared with the impersonal order of nature of Spinoza and Laplace the property of embracing in one timeless act the whole history of the universe.'" According to Capek (1961: 161), the spatialisation of time leads to actually rejecting its reality - the belief that the true reality is timeless, and change and succession merely apparent, a conception rooted in the Eleatic tradition of thought, which reappears under various terminological garments in the writings of such different authors as Plato, Damascius, lamblichus, Plotinus, Kant, Spinoza, Einstein, Weyl, and Eddington, to name but a few. It is also displayed in Laplace's (1814: 2) idea of totally pre-determined future of the physical world, a vision of reality in which the difference between past and future events is reduced to merely our "incapacity to know everything at once": Tous les evenements, ceux meme qui par leur petitesse semblent ne pas tenir aux grandes lois de la nature, en sont une suite aussi necessaire que les revolutions du soleil. Dans ignorance des liens qui les unissent au Systeme entier de 1'univers, on les a fait dependre des causes finales, ou du hasard, suivant qu'ils arrivaient et se succedaient avec regularite, ou sans ordre apparent; mais ces causes imaginäres ont etc successivement reculees avec les bornes de nos connaissances, et disparaissent entierement devant la saine philosophic qui ne voit en elles, que l'expression de l'ignorance ou nous sommes des veritables causes. 4.2.4.8. Time as the fourth dimension of space This section deals with the tendency to spatialise time by treating it as another, fourth dimension of space.160 In physics, it has found conceptual support in the graphic representation of time.

158 159 160

E.g. in Molchanov's, cited in Akhundov 1986. Capek 1961: 163. That this tendency exists prior to and independently of the need to represent time in scientific research may be illustrated by the idea of "time travel" - Wells' "time traveller" becomes transferred into another time without any changes to himself, that is, as during a journey in space.

Ill

In this century, the extreme conception that time is literally another dimension of space has occasionally been put forward, with the resulting denial of the reality of changes in the world and their relegation to the psychical sphere. A similar rejection of the reality of time by some authors has been produced by the spatialisation of time in the spatial representations of relativist space-time. Pre-relativist graphic representations of time The earliest known attempt to graphically symbolise time stems from Zeno, who depicted it as an infinitely divisible straight line. As kinematics became the core of mechanics by taking motion into consideration, time entered physics as a basic concept. Descartes was the first modern philosopher to geometrise time in the co-ordinate system bearing his name, in which time was represented as one of the spatial axes in the form of a straight line. It gave time a representation which is static and in which the distinction between space and time as two separate modes of correlating and ordering phenomena (juxtaposition vs. succession) becomes blurred. In symbolising time by the axis t (of independent variables) there was at first no conscious attempt at spatialising time. The dynamic and progressive character of time was symbolised by an ideal motion of the pointlike present sliding along the time axis from the past to the future. But in contemplating a spatial diagram of temporal processes it is easy and psychologically natural to forget its underlying dynamic meaning. We may assume that the spatial symbolism has made its contribution to the tendency to forget the essential difference between the past, present, and future by reducing them to simple differences of position. Thus, the spatial diagram, like the religious image of eternity from where everything may be seen at once supports conceptually the Laplacian notion of the timeless order of nature. Descartes, and later d'Alembert, called duration "the fourth dimension", and Lagrange characterised mechanics as a "geometry of four dimensions". This way of conceiving time was in a way preparing the way for the Laplacian vision of reality. Time as the fourth dimension in relativity Before relativity, the universe was regarded as a Euclidean container of juxtaposed simultaneous states of affairs. Space, using Capek's spatial metaphor, is an instantaneous "cut through" the cosmic becoming. This attitude to space depended on a commonsensical extrapolation of the features of space known from the "world of middle dimensions" to the whole of space. The Euclidean character of space, immediately available in experience, was generalised to the whole universe. The cosmos was conceived as a homogenous container of space and matter. Relativity questioned the very existence of space as a container of states of affairs because in relativity there is no absolute simultaneity of distant events, that is, there is nothing like the state of space existing at a given moment - it becomes meaningless as soon as we abandon the idea of a given moment in time. In relativity, the conception of space "going through" successive moments of time and assuming successive states gives place to spacetime, a single dynamic entity. However, in the relativistic representation of space-time, the tendency to spatialise time by rendering it as the fourth dimension of space becomes reinforced rather than eliminated. Representing time as another dimension hardly distinguishable from the three spatial dimensions, was entrenched by the visualisation of the space-time fusion in the diagram pro-

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posed by Minkowski in 1908 which bears his name. The atemporal Minkowski diagram represents time in a picture containing a pictorial element labelled t. It spatialises time. The theory of relativity shows that, within certain limits, no absolute distinction can be made between temporal and spatial components of an interval, either on this diagram or in experience. The conceptual representation of space-time as a kind of space finds its linguistic realisation in metaphorical expressions like: Space ... is not a given entity like the earth; it is space-time that is given, and space must be sliced off from space-time. And if there is one way of doing the slicing, there are many.161

An illustration of the explanatory value of the visual representation of space-time as fourdimensional space, which makes it visualisable and, thus, conceptually manipulable by a layman, may be this brief explanation by Smart (1964: 11-12) of why observers moving at different velocities make different judgements about the simultaneity of distant events: We can consider a four-dimensional space, three of whose dimensions correspond to space in the ordinary sense of this word, and one of whose dimensions is taken to be a time dimension. An instantaneous state of space ... is given by a three-dimensional cross section of this four-dimensional space-time ... we can think of man or star as a very elongated four-dimensional worm ... Two stars which are in uniform velocity with respect to one another and which are not accelerated with reference to our frame of reference, will appear in the space-time picture as two very long straight worms inclined at a certain small angle to one another. An observer on each star would regard himself as at rest. He would therefore take his world-line ... as his time axis. It would be natural to suppose that he takes his space axes as, in a certain sense, at right angles to this line. In other words, observers on stars whose world lines are inclined to one another will slice the four-dimensional cake at different angles: they will regard different sets of events as simultaneous to one another, (emphasis HP) 4.2.4.9. An excursion: misconceiving time as space The tendency to conceive time as an additional fourth dimension of space, following from the visualising of space-time in relativity, is a frequently committed error. Numerous physicists, such as Paul Langevin, Meyerson, Einstein, Schlick, Bridgman pointed out in their writings the misconception resulting from this way of speaking. One effect of the conceptual spatialisation of time in Minkowski's space-time representation of physical becoming is the tendency to forget that space-time cannot be conceived as an entity enduring in time. Such a conceptualisation is subject to the already mentioned fallacy, i.e., the tendency to introduce the time factor twice into the representation. This often happens in popular expositions of relativity. It is sometimes said that a light signal is propagated, or moves, from one part of space-time to another. In fact, the "correct" way to express the state of affairs which these and similar formulations are meant to describe would be to say that the signal lies between two regions of space-time. The "dynamic" way of speaking of events in space-time corresponds to the linguistic and conceptual tendency already pointed to in the commentary on Newton's linguistic treatment of light in "Opticks". Words such as "path" and "follow" with which the behaviour of light (or other objects) in space-time is referred to have both static and dynamic meaning, or, in an alternative formulation, a meaning neutral with respect to actual movement: 161

Barman 1970. Quoted in Hinckfuss 1975: 82.

113 Follow me. In the south, the political border of the country follows a natural border between the lowlands and Tatrak mountains. Similarly, "path" may refer to both a static object and the sequence of all the points which a moving object has passed through.162 This property of language makes it easy to overlook the difference between the space-time representation of becoming, which is static, and the usual space in which things move: Light rays too must follow geodesies in space-time ... [...] The earth follows a straight path in four-dimensional space-time.'"

Schlick (1964: 293) expressed his reservations regarding the dynamic way of speaking about the space-time representation of physical events saying: One may not, for example, say that a point traverses its world-line; or that the three-dimensional section which represents the momentary state of the actual present, wanders along the time-axis through the four-dimensional world. For a wandering of this kind would have to take place in time; and time is already represented within the model and cannot be introduced again from outside.

We have already mentioned another, related aspect of the misconceptions arising from the spatialisation of time. If we take the model for the thing modelled, the difference between future and past vanishes, becoming purely conventional, and we are once more reminded of Laplacian determinism. Such an interpretation of space-time led also some contemporary relativist physicists to the relegation of time as a relation of succession, contrasted with juxtaposition which is a property of space, to the sphere of cognition, an idea which already appeared in philosophy in the antiquity: Ahl (1985: 279) quotes the Neoplatonic philosopher lamblichus saying that "we experience in succession the coexisting points of intellectual time". History notes at least one major case of the idea that time is literally the fourth dimension of space: it was propagated in the 1920's by the psychologist Ouspensky in his widely read "Tertium Organum" (1923, 1981), a project in conceptual and linguistic sort-trespassing in which the use of spatial terms is pushed to its utmost limits (by mixing up optical, psychological, spatial and time-referring notions). Ouspensky was inspired by C. H. Hinton's (1906 and 1910) concept that the "true" space we are immersed in is in fact four-dimensional, and only our imperfect perception prevents us from perceiving directly the fourth dimension of space. The only way we can get some knowledge of it is through "time experience in threedimensional space":164 the fourth dimension of space is experienced as a duration of a threedimensional object in time. From the definition of a surface as "a relation between two things"165 and the existence of physical facts grouped together under the name of surface tensions, Hinton concludes that "it may be well that the laws of our universe are the surface

162

This property of language and cognition is based on a "transformation scheme", in the sense of Lakoffand Johnson 1980, which seems to be universal rather than conventional. Speed lines, e.g. in comic strips, representing the path of movement of speedily moving objects, are reported to be understood by young children and the blind without prior instruction. "' Hawking 1988: 31. 144 Hinton 1906: 207. 165

Hinton 1910: 9.

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tensions of a higher universe"."6 The ether which we customarily think of as filling the universe may be the surface of contact of two higher-dimensional bodies, or universes. Ouspensky identifies Hinton's "fourth dimension" with time itself. What follows is the denial of reality of time as a mere appearance arising out of the restrictions on human perception - time is relegated to the realm of psychology. If time is another dimension of space, the reality of motion must be denied because it puts forward a demand for a new time, as no motion can take place without time; motion, then, is a psychological illusion; "... in reality, there is only extension in a direction we are unable to imagine". Among contemporary physicists, Jones (1982), admitting his debt to Ouspensky's speculations, subscribes (seriously? - who knows!) to his vision of reality in which the notion of time as the fourth dimension of space is taken literally and the difference between time and space is relegated to the sphere of consciousness. Also for Jones, our sense of time is an imperfect perception of the four-dimensionality (or multi-dimensionality) of the spatial universe.168 Although relativity does not treat time as actually being another dimension of space, a view Jones (following Ouspensky) seems to seriously consider, it represents it as such. As a consequence, the difference between the represented and the representation frequently becomes forgotten. The reality of time is denied in favour of a view that it is a psychological phenomenon. In his popular exposition of relativity, Zukav (1979:194-195) describes the difference between Newtonian time and Einstein's ideas in similar terms: The Newtonian view of space and time is a dynamic picture. Events develop with a passage of time. Time is one-dimensional and moves (forward). The past, present, and future happen in that order. The special theory of relativity, however, says that it is preferable, and more useful, to think in terms of a static, non-moving picture of space and time. This is the space-time continuum. In this static picture, the space-time continuum, events do not develop, they just are. If we could view our reality in a four-dimensional way, we would see that everything that now seems to unfold before us with the passing of time, already exists in toto, painted, as it were, on the fabric of space-time. We would see all, the past, the present, and the future with one glance, (italics in original) Zukav's commentary juxtaposes the Newtonian view and the relativistic representation of relativity as a dynamic and a static picture, respectively. The use of the expression "spacetime picture" is symptomatic here: pictures are spatial objects that persist in time and can be contemplated in time either in toto or sequentially. What happens here is the following: the static character of the representation of space-time becomes mistaken for the static character of space-time itself. The word "static" brings in its usual meaning - unchanging in time. Thus, speaking of the static character of space-time leads to conceiving of it as an object persisting in time because time is part of the meaning of "static". As an object in time, spacetime could (if we were not built the way we are) be perceived and apprehended in toto. What results is the Laplacian predetermined universe. This misconception is rooted in the tendency 166 167 168

ibid: 52. Ouspensky 1923, 1981:31. Imagine a cigar-shaped object passing through a two-dimensional plane of creatures whose perception is confined to two dimensions; the passage of the object through the plane seems like a sequence of birth, growth, decrease, and disappearance of a circular object. By analogy, phases in time may be conceived as cross-sections of four-dimensional objects. "The potential nature is manifested to us in time as a process of unfolding and developing, a sequence of stages, a history ... Perhaps in some higher state of human consciousness, one would not experience this apparent evolution; one would see the totality, the whole cigar, as it were, and not only its changing cross sections." Jones 1982: 85.

115 to forget that the act of perceiving and apprehending anything is a physiological process, that is, it happens in time;169 therefore, the very notion of "viewing" space-time in toto includes the time factor twice - once as a part of space-time and once in the process of observing space-time "from outside" as a static "picture". Similarly, relativistic physicists as Eddington (cf. page 103) and Weyl tend to take the spatialisation of time literally (as the fourth dimension of space), which appears in the spatial representation of space-time. Weyl says: The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upon the life-line of my body, does a section of the world come to life as a fleeting image in space which continually changes in time.170 Like lamblichus in antiquity and Laplace in the 19th century, Jones, Eddington, and Weyl eliminate time from the physical world and transfer it to the consciousness, moving toward the future. In doing that, these authors introduce a dualistic spatialised picture of time: there is a timeless, exclusively spatial four-dimensional physical world and a temporal consciousness. Criticising Weyl, Capek (1961: 165) speaks of "an absurd dualism of the timeless physical world and temporal consciousness, that is, a dualism of two altogether disparate realms whose correlation becomes completely unintelligible ..." The notions of a timeless physical world and temporal consciousness are incompatible because the very idea of 'consciousness creeping along the world line' implies a process taking place in time, that is, something which the static representation aimed to eliminate. Mistaking the static character of the spatial representation of space-time for the property of space-time itself, such conceptions bring with them the tendency to conceive of motion with respect to the "static" space-time. But the very notion of movement implies time: an object which moves along "the fourth dimension" must take time for its travel. The difficulty is unavoidably present in any theory resolving time into space.'71 4.2.4.10. The metaphor of space-time curvature The term "curvature" originally applied to surfaces (and lines) in Euclidean geometry. After the invention of non-Euclidean geometries, the term "measure of curvature", or, simply, "curvature", at first merely applied, (i.e. used in its original meaning) to the surfaces of Euclidean model of a non-Euclidean plane, became generalised to describe a value "k" of 169

170 171

The very idea of absolute time depends to a large extent upon this tendency to forget the time aspect of cognition. We can conceive of time as independent of happening because we are able to entertain the image of the flow of time in a motionless universe, that is, to conduct a Gedankenexperiment in which the universe is standing still and nothing is happening but the passing of time. What we easily forget is that we as observers and the process of observation (perception), are both contained within the picture. The process of observation, however, is not independent of happening, because human consciousness is a fact of physiology as much as a spiritual act, so the persistence of a conscious subject means that there is a process taking place. Imagining ourselves "observing" the motionless universe, we make the flow of time depend on the flow of consciousness, which "flows in its even tenor" even if nothing else does. By eliminating the process of observation from the picture, reminiscent of that described as a fallacy of classical physics from which modern quantum theory had to liberate itself before it could become conclusive about wave/particle dualism, we are prone to admit that time would be passing even in a motionless universe. This is a result of the failure to notice the unavoidable projection of the human factor into the world of things, similar to that which, in a more overt way, underlies personification. Weyl, quoted in Park 1972,1: 110. Cf. Chari 1949.

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non-Euclidean planes analogical to the curvature of planes in the Euclidean representation. The border between the application and extension or transfer of a concept appears in this case to be particularly narrow. This probably contributes to the fact that the term "curvature" as it is used with its new, generalised reference, can hardly defend itself against the heritage of connotations from its original meaning. Assuming that the structure of space-time is non-Euclidean, relativity took the expression from the field of pure mathematics and used it for the description of the physical world. After its introduction, space began to be described as "curved" in the fourth dimension. Gravity is customarily described as the effect of the fact that space-time is not flat, as had previously been assumed; it is curved, or "warped", by the distribution of mass and energy in it.172 This way of speaking is not confined to popular scientific texts, but has also been imported to expert communications, as for example in the specialist article by the same author entitled "Operator Ordering and the Flatness of the Universe" (Nuclear Physics B 264, 1986: 185). Consequently, The rapid expansion [of the universe] causes the space to become flatter, just as the surface of a balloon becomes flatter when it is inflated.173 The process of inflation [of the universe] first smoothes out any primordial inhomogeneities that might have been present in the initial conditions.174 The words "bent" or "curved" bring in their usual associations, suggesting an image of a "bent" sheet which is different - convex vs. concave - on both sides, which is not true of the planes of non-Euclidean geometry, which are identical on both sides. The word "curvature", in its original (literal) sense, applies only to surfaces of a Euclidean model of a non-Euclidean plane. Carnap (1966: 142-143) comments upon the transfer of the word's meaning from Euclidean planes to four-dimensional space-time: ... the term 'measure of curvature', as applied to non-Euclidean planes, does not mean that these planes 'curve' in the ordinary sense. Generalising the term 'curvature', so that it applies to non-Euclidean planes, is justified, because the internal geometrical structure of a Riemannian plane is the same as the structure of the surface of a Euclidean sphere; the same is true of the structure of the plane in Lobachevski space and the surface of a Euclidean pseudosphere. Scientists often take an old term and give it a more general meaning ... The trouble began when Einstein made use of non-Euclidean geometry in his general theory of relativity ... Books were written explaining these things to the layman. In those books, the authors sometimes discussed 'curved planes' and 'curved space'... Popular writers said that Einstein had discovered that the planes in our space are curved ... Such talk of curved space led people to believe that everything in space is distorted, or bent... All this could be avoided if the term 'curvature' had been avoided. On the other hand, to introduce a term entirely different from one already in customary use in mathematics is not easy to do. The best procedure, therefore, is to accept the term 'curvature' as a technical term but clearly understand that this term should not be connected with the old associations ... We must remember that this is curvature in a technical sense, and is not quite the same as our intuitive understanding of curvature in Euclidean space. We shall discuss the educational uses of the metaphor of "curved space", developed out of the transfer of the term "curvature" to non-Euclidean geometries, in the section dealing with educational metaphor. 172 173 174

Hawking 1988: 29. ScAm, May 1985: 96. ibid.: 97.

117

4.2.5. Container and orientational metaphors in quantum mechanics We will show in the example of the rendering of energy in quantum mechanics how the orientational and container metaphors ubiquitous in everyday language also come to be applied in concept formation in physics. It will also be noted that in the non-formal description in popular scientific texts on quantum mechanics, written in a non-specialist variety of general language, the same underlying spatial metaphors are used to generate innovative metaphorical expressions (novel satellite metaphors) as have been productive in shaping theoretical concepts in this field. In generating verbal physical descriptions, quantum mechanics uses metaphorical devices omnipresent in everyday language such as • the application of verbs of movement to speak of changes, • the use of orientational adjectives and prepositions to characterise relations between states of affairs, • conceptualising characteristics of systems as states in the form of spatially arranged containers This metaphorical aspect of specialists' language is a natural continuation of the way we talk about changes and relations in non-scientific contexts, rooted in underlying metaphors and illustrating Schön's (1963: 60) contention that metaphors are not to be located on the level of particular verbal expressions, like words or phrases: ... from a symbolic relation, once established, an indefinite number of possible related aspects of the new situation can be generated and considered.

4.2.5.1. Visual rendering of energy The visual representation of physical relations and processes reinforces their conceptualisation in spatial terms. The quantum mechanical conceptualisation of energy in spatial terms is supported by visualisations of two kinds: - the observable spectrum of electromagnetic radiation emitted or absorbed by chemical samples, - graphical representation (a diagram plotting the energy of an elementary particle against its position). Both of these contribute to the conceptualisation and wording in which quantum mechanics describes the processes involving the concept of energy. In what follows we will consider the band model of solids, whose basic concept of "energy band" is rooted conceptually in the phenomenon of the observable spectrum of electromagnetic radiation, as an incorporation of conceptual spatial metaphors. Further, we will consider the terminology of quantum mechanics used in the description of the energy potential field and the contribution to it of the graphical representation of energy (diagrams plotting energy against position). 4.2.5.2. Ranges and states: containers of physical processes One of the very basic tools in the analysis of and the communication about physical processes is the conceptualisation of values or ranges of values of parameters characterising a

118

physical system through the ontological and spatial metaphor of state conceived as a receptacle of this physical system. The very concept of state experienced a far-reaching development with the advent of modern science when it became extended to the process of movement. Initially, "state" (Lat. status) was coreferential with "static", meaning unmoved, being in the same position in space. Conceiving movement as a state means that the meaning of the notion of "state" no longer includes identity of position in space at that stage. The concept of "the state of movement" appears in Newton's "Principia": "Every body ... continues in its present state, whether it be of rest, or of moving" (Law I). Here, the word "state" no longer implies the constancy of position. According to Cassirer (1957: 15-17), this conceptual change was associated with Galileo's mathematical analysis of movement of a physical system and lifting it to the position of a central aspect of its physical existence. The notion of movement as a state of a physical system conceptually paves the way for extending the notion of "state" to other properties of a physical system, so that it can refer not only to these properties which remain constant, but also to changes which a system undergoes, as in: chaotic state; vibrational state; transition state of quantum chemistry. "STATES ARE CONTAINERS" is closely related to a metaphor rendering (onedimensional) RANGES of values of physical parameters as REGIONS or EXTENDED OBJECTS. The word "region" is often used as a synonym for "range". Such an application of the term "region" violates two of its semantic restrictions: extension in physical space and the condition of having two or three dimensions. In the same way, the name "space" has been transferred to conceptual and mathematical "spaces" of any number of dimensions which are not spatial dimensions but are used to describe physical attributes of a system, such as the statistical distribution of momentum in a gas of particles, or color attributes. Ranges conceptualised as regions not only contain certain values of parameters but may also "contain" the physical systems characterised by these parameters. STATES ARE CONTAINERS and RANGES ARE REGIONS/EXTENDED OBJECTS/CONTAINERS are reformulations of the same underlying conceptualisation, the notion of state being however a case of more pronounced hypostasis: states are more thing-like conceptualisations of physical attributes. The STATE=CONTAINER metaphor works by being inseparably coupled with CHANGE=MOVEMENT. We talk of physical systems as being in a certain state, leaving one state and entering another, transition from one state to another. This is the way in which we conceptualise the staying the same or the change of parameters. 4.2.5.3. State as container in quantum mechanics The concept of state is an ontological entity-making metaphor. In quantum mechanics, a basic "state" concept is that of the energy state. Consider an example from the language of quantum mechanics, where energy states of molecules and elementary particles are spoken of in terms of movable objects: The shallow acceptor removes an energy state from the valence band and establishes it as a quantum state of lower energy in the gap region. '"

175

Encyclopaedia of Physical Science and Technology. 1987, 5: 303-304.

119

Through being made into an entity, a state becomes commensurate with the notion of a material particle: What makes an excited state interesting is that it may be understood as a particle. "6 By being made into entities, states may be described as interacting with each other or with other entities: The blue light interacts with the vibrational state of the molecules in the sample and appears as a scattered green light.177 We want to consider structures ... with relatively weak interactions between electronic states of different layers.178 Moreover, they become quantifiable: . . . equal amounts of the vertically polarized state and the horizontally polarized state 179 ... The concept of state is structured by a spatial metaphor. States are spatial entities characterised by an extension in space and the container structure: the population of the excited state180... the probability that a single molecule will occupy the excited state'81 ... The linguistic reformulation of a number of parameters characterising a physical system (object) as a state containing this system is amply illustrated by the two alternative formulations of the Pauli principle, applied to electrons in an atom or another quantum system: The Pauli principle ... says that no two electrons in a system can have the same set of quantum numbers."2 becomes reformulated as The Pauli principle permits only two electrons to occupy each state in k-space.183 No two electrons in an atom can have the same set of quantum numbers n, l, m 1, and m2; or no two electrons in an atom can exist in the same state.184 4.2.5.4. Bohr's model of atomic structure The basic concepts concerning the structure of a single atom originated within Bohr's early "solar system" model. In this model, electrons orbit the nucleus along orbits lying at different distances from it; each orbit corresponds to a different energy level. The state of an atom in which the electrons are in the state of lowest possible energy is called the ground state (most probably coined by Bohr in 1926), the term being derived from "MORE IS UP" (more energy is higher, less energy is lower) and also consistent with 176 177 178 179 180 181 182 183 184

ScAm, March 1984: 70. ScAm, April 1984:47. Phys. Stat. Solidi (b) 52, 1972: 79. ScAm, Jan. 1988: 37. ScAm, Feb. 1984:71. ibid.: 72. Encyclopaedia of Physical Science and Technology, 11: 464. ibid., 4: 647. Weidner and Sells 1973: 696.

120 the orientation "less distant from the centre = higher", imposed upon the atom by analogy with a system in which the gravitational force of a massive body such as a sun (or the earth) causes smaller objects to orbit around it or, in the limiting case, to fall down to the ground, to the minimal possible level of potential energy. If an electron in an atom is in a higher state of energy, we speak of the excited state of an atom: in this term, "MORE IS UP" (more energy is higher) combines with "EMOTIONAL IS UP", producing "MORE IS EXCITED". In this early model, electrons surrounding an atomic nucleus are grouped into a series of shells centred on the nucleus, each shell having a characteristic radius and energy. (Today, an electron shell is taken to signify all those electrons in an atom which have the same principal quantum number.) At the same time, the electrons placed in different shells situated in the space surrounding the atomic nucleus are represented in the model as occupying different energy levels: We shall now put a single electron on atom j into an energy level Ei ... 18S . . . most levels become depopulated .. ."* The electron shell is a common kind of catachresis transferring the name of a familiar object to an element in a model taken to correspond to an element of the object in study, which need not interest us at this point. The calculated distances between the shells and nucleus can be interpreted as distances in real physical space. The "levels" of energy, on the other hand, refer to energy distribution and only secondarily to the distribution of the physical space. The concept of the energy level is a satellite metaphor derived from the underlying "MORE IS UP" metaphor. This underlying metaphor is conceptually consistent with the planetary model of the atom in which "higher" is interpreted as "more remote from the centre". Higher shells correspond to higher energy levels. The increase of energy of an electron in an atom is represented in the models of the atomic structure as a transition from a region (shell) closer to the nucleus to a region more distant from it. The language of physics applies the underlying metaphors of state and movement to reformulate this "literal" transition of an electron within the spatialised model (whose reality status we cannot discuss here), re-construing the actual space surrounding the nucleus, as a transition of an atom from one state to another. (Interestingly, we are dealing here with a superposition of two figurative conceptualisations, the solar system model of an atom becoming itself the recipient subject in the metaphor.) MORE IS UP, STATE IS CONTAINER, and CHANGE IS MOVEMENT combine to produce a way of speaking in which the changes of a physical parameter - the energy of an atom - are rendered as movements between spatially ordered areas or containers: When an atom undergoes a transition from an upper energy state to a lower energy state, a photon of energy is emitted.187 4.2.5.5. Energy states of elementary particles Not only atoms, but also elementary particles, e.g. electrons in a solid, are characterised as being in different energy states, characterised again by '"' Solymar and Walsh 1979: 129. ScAm, Feb. 1984:72. 187 Weidner and Sells 1973:688. 186

121 - extension: For the observation of discrete subbands ... it is necessary that the states are not broadened too much by electron-photon interaction.'88 From any two quantum states of a system further states can be formed by superimposing them. Physically the operation corresponds to forming a new state that Overlaps' each of the states from which it was formed.18* Each state is split into a set of N substates."0 - container structure: By using a superposition principle one can form a quantum state that contains equal amounts of the vertically polarized state and the horizontally polarized state.'" There are no nearby unoccupied states for transitions."2 As the temperature is reduced through the superconducting transition, we speak of the condensation of the electron system into the paired state.1" Similarly, the underlying container metaphor supplies the name to a phenomenon known in the terminology of particle physics as "Bose-Einstein condensation", referring to the "aggregation" of bosons, a type of elementary particle, in "low-energy states", (or, in an alternative formulation, in a certain region in conceptual momentum space). Since the state of low energy (momentum) is conceived as a container of bosons (and a region within the momentum space), many bosons being in this state means that they are densely packed -> condensation of elementary particles in a low-energy state. 4.2.5.6. Band model (theory) of solids The spectra of electromagnetic radiation emitted (or absorbed) by material samples consist of bands of different colours in which each colour corresponds to a different range of wave length, related to different values of radiation energy. These observable bands provide the concept of electronic energy consisting of spatially arranged "energy bands", composed of a sequence of energy states, or levels, as containers of electrons. The description of spatial relations within the visible emitted spectrum of energy goes seamlessly over into the spatial conceptualisation of energy itself: ... discrete energy levels ... are packed so tightly together that they cannot be resolved."4 The spacing of vibrational energy levels is of order of a few tenths of one eV and the most important vibrational spectra occur in the near and middle infrared regions."5 Each state is split into a set of N substates. In a solid of appreciable size ... the substates are so numerous and so closely spaced in energy .. ."*

188 189 190

'" '" "" 194

"" "*

Physica Status Solidi (b) 52, 1972: 88. ScAm, March 1988: 36. ScAm, Nov. 1983: 118. ScAm, Jan. 1988:37. Encyclopaedia of Physical Science and Technology, 11: 468. ibid. ScAm, April 1984: 47.195 Christophorou 1971: 67. Christophorou 1971: 67. ScAm, Nov. 1983: 118.

122 The band model of solids applies the concept of "energy band" together with the ubiquitous underlying conceptual metaphors of "STATE IS CONTAINER", "CHANGE IS MOVEMENT", and "MORE IS UP". In this model, the notion of "energy band" refers to the ranges of energy available to electrons in a solid. The meaning extension of "band" to "range" occurs in everyday language and is listed in the Oxford English Dictionary, 2nd edition, as a figurative meaning of "band": BAND sb. 2 \Qb fig. = RANGE. 1928 A. Lloyd James in S.P.E. Tract, xxxii. We now have a certain type, or rather a carefully chosen band of types of English. 6 Those who speak any one variety of the narrow band are recognised as educated speakers. 1959 Listener 19 Feb. 331/I The standard of play ... is at a fairly level band of skill and teamwork throughout, at least in Division One ... "Band" figuring for "range" within a physical term appears in the notion of frequency band applying to radio waves: band

Electr. a range of frequencies or wavelengths that falls between two given limits; waveband."7

In the specialists' language of quantum mechanics, the notion of a range of electronic energy is replaced by the figurative notion of a band leading to a visualisable model. The quantum mechanical band model of solids defines the following terms applying the word "band" to refer to the range of energy: conduction band:

1. In a semiconductor, the range of electron energy, higher than that of a valence band, possessed by electrons sufficient to make them free to move from atom to atom. When they leave the valence band, the are free to move under the influence of an applied electric field and thus they constitute an electric current. 2. In the atomic structure of a material, a partially filled or empty energy level in which electrons are free to move, thus allowing the material to conduct an electric current upon application of an electric field by means of an applied voltage."8

electron energy band:

one of the bands or zones of electron energy levels in a crystal by which the total range of energy states is broken up into alternate allowed and forbidden ranges. The extent of these allowed and forbidden bands is determined by the nature and structure of the crystal. A filled band is an allowed band in which all energy levels are occupied. An empty band is one in which none are occupied."9

energy band:

a specified range of energy levels that a constituent particle or component of a substance may have. The particles are usually electrons, protons, ions, neutrons, atoms, or molecules. Some energy bands are allowable and some are unallowable for specific particles. For example, electrons of a given element at a specific temperature occupy certain energy bands. Examples of energy bands are the

197

O.E.D., 2nd edition. "8 Fiber Optics and Lightwave Communications. Standard dictionary. 1981. 199 Concise Dictionary of Physics. 1979.

123

higher and lower energy ranges of the conduction and valence bands.200 valency band:

(1) the range of energy states in a solid crystals in which lie the energies of the valency electrons. (2) The band below the conduction band in an insulator or semiconductor.1" In a semiconductor, the range of electron energy, lower than that of the conduction band, possessed by electrons that are held bound to an atom of the material, thus reducing conductivity for electric currents even under the influence of an applied electric field. When electron energies are raised (e.g., by thermal excitation or by phonons), electrons with the highest energy levels of the valence band are raised to the lower energy levels of the conduction band, thus leaving holes in the atoms whose electrons remain in the valence band. The valence band energy level is below the conduction band. In a conducting material ... the valence band energy level is above the conduction band (i.e., the conduction band is lower), thus allowing the electrons to be more free to move as an electric current.186

band-edge energy:

the band of energy between two defined limits in a semiconductor. The lower limit corresponds to the lowest energy required by an electron to remain free, while the upper one is the maximum permissible energy of a freed electron.342

The notion of "energy bands" referring to the ranges of energy of the electrons in solids appeared for the first time in Morse's article on the quantum mechanics of electrons in crystals in 1930. Previously, Bloch (1928) had shown on the basis of the Pauli principle that the ground state energy level EO of an isolated atom gave rise to G3 energy levels in a metal containing G3 atoms. With the idea of the splitting of the set of energy states available to electrons into a number of subsets of possible energy values and a number of subsets of "disallowed" values, the spatial metaphor of a band emerges: ... the energy level corresponding to the nth quantum state of a free atom will be split into a large number of very slightly separated levels; in fact, if the crystal is considered infinite in extent, the levels of the free atom will be spread into bands of allowed energies which may or may not be separated from their neighbours by bands of forbidden energies.201 This means that the periodic variation of potential inside the crystal creates bands of forbidden energies inside the crystal... wide for low energies, but... narrow for higher energies.202 This way of conceptualising energy is a matter of invention rather than necessity, but the invention is so deeply rooted in the existing patterns of thought as to be natural and hardly noticeable. For comparison, at about the same time, Kronig and Penney (1931: 502), also writing about the same problem of discontinuities in possible electronic energy values in crystals, used alternative formulations and spoke of "pieces" within the "energy spectrum" rather than bands of energy: The energy values which an electron moving through the lattice may have, hence form a spectrum consisting of continuous pieces separated by finite intervals ... 200 201 202

Dictionary of Electronics and Nucleonics. 1969. Morse 1930: 1311. ibid.: 1315.

124 This is illustrated by a diagram in which the discontinuous ranges of possible electronic energies are represented as strong segments on the horizontal axis ßa. At other points, however, the authors, in referring to the diagram, speak of regions rather than pieces (or ranges), applying the word "region" in a way based on RANGES ARE REGIONS: We may enquire after the density distribution of the energy values in the allowed regions of ba . . . [...]The binding has thus the effect of concentrating the stationary states at the limits of an allowed region.203

Furthermore we have plotted in fig. 6 the values of (symbols) as a function of ßa when a is a state in the first allowed region while a' is that state in the second negative, third positive and fourth negative allowed region.204

As noted before, the word region is frequently used to denote a range of numerical values; here, it might have received an additional impact from the fact that the strong pieces on ßa represent sets of states, and, as we saw before, states are themselves containers and possess extension. The rendering of the ranges of allowed energy values as regions permits the rendering of the change of velocities of moving electrons as the electrons moving between the regions (ranges) of allowed energy values: When the velocity begins to extend that corresponding to the upper limit of a forbidden interval in the energy spectrum of the crystal, the impinging electron can enter into a new region of allowed energy values ... [...]Perhaps, also, the constant energy losses of electrons impinging upon incandescent metals ... may be interpreted as corresponding to the transfer of the conduction electrons to the higher allowed regions of energy.205

The concept of an energy band is a further development of the hypostasis making ranges into regions consisting of states. The underlying container metaphor is made more explicit in the concept of band than in the concept of state because band is more obviously a spatial and visualisable concept. The underlying spatial concept manifests itself not only in the verbal representation of the phenomena in question but also through visualisation with which it is intrinsically connected. The concept of energy bands is a self-explanatory result of the idea of discontinuities in the permitted values of electronic energies in a solid because these energies had already been previously conceived of (verbally expressed) in spatial terms (states, levels, regions), although possibly involving a lesser degree of visualisation. What results is the model in which electronic energy consists of energy bands possessing a certain width, separated by gaps and composed of a sequence of energy levels, or states which are containers of electrons. The underlying metaphor STATE=CONTAINER and the associated CHANGE IS MOVEMENT are firmly anchored in thought and language making the spatially conceived band model of solids an almost self-evident expression of the discovered underlying structure of the observed phenomena. The metaphorical model based on the underlying metaphors of general thought and language offers verbal access to the phenomena under study in common language, and the words of common language retain at the same time their general meaning and function as carriers of specialised meanings. 203 2M 205

Kronig and Penley 1931: 504. ibid.: 505-506. ibid.: 512.

125

The metaphorical character of the notion of a "band" (the far-reaching meaning extension of the word) becomes immediately apparent if we consider that the expression "energy bands" refers to one-dimensional objects and yet, the only dimension of these objects is called width rather than length, which violates the usual semantic restriction on the use of "width": the sole dimension of a one-dimensional object is usually called its length (cf. Clark 1973). We are dealing here with a visualisation which makes one-dimensional ranges into twodimensional objects whose physical description is conceptualised as width and whose length is neither physically provided for nor conceptually specified. Morse's new terminology based on the band model quickly found its way into the mainstream of specialists' language. The citations below come from a study by Wilson dated 1931: The action of a field is to accelerate or retard the electrons, causing them to make transitions from one set of energy levels to another. This can only happen if the final energy levels are already occupied ... it is only in the neighbourhood of the critical energy that the energy levels are partly filled and partly empty.206 It appears that the energy levels break up into a number of bands of allowed energies, separated by bands of disallowed energies, which may be of considerable width . . . [...]When the temperature is different from zero there will be a few electrons in the second band and a few vacant places in the first band, and conduction will take place.207 Wilson's (ibid.: 460) new suggestion is that in the case of three dimensions, the problem is not quite so simple, for although there are discontinuities in the energy it is sometimes possible for the energy to take every value between a minimum value and infinity. In his article on the history of early quantum mechanics, Wilson (1980: 47) speaks of his having suggested, in the discussion with Bloch shortly before writing his article on semiconductors, that "the bands can overlap", which is correct as far as the physical contents is concerned but not quite so correct linguistically; in the written form, the notion of the "overlap" of "zones" of energy in abstract mathematical space appeared probably for the first time in Brillouin (1930)208 and has been widely used ever since. Physics today continues to describe the conduction phenomena in terms of the band model, actualising the underlying container metaphor: In a semiconductor the ground state is actually a band of states that exist over a range of energies called the valence band ... Likewise the excited state of a semiconductor is actually a band of states existing over a range of energies called the conduction band.20" The picture that thereby emerges is that of groups of closely spaced discrete allowed energies that can be populated by electrons, with the groups of allowed levels being separated by energy ranges called gaps.210 An energy band is found to contain one allowed state per atom ... 2 " The same spatial language is to be found in the popular scientific description of the phenomena in question: 206 207 208 209 210 211

Wilson 1931:458. ibid.: 460-461. These zones are known today as Brillouin's zones. Encyclopaedia of Physical Science and Technology, 11: 508. ibid.: 466. ibid.: 468.

126 The states of lowest energy are fully occupied ... hence the valence band is full. 212 The basic theoretical prediction is that the band gap leading to electronic insulation in a solid can be narrowed at high pressures and finally squeezed out.213 ... energy greater than the width of the band gap .. .214 The underlying metaphor "more is up" imposes the vertical orientation upon this arrangement: ... to fill every energy state up to the start of a given energy gap .. .21S Excited states of the exciton lie below the band-gap energy of the semiconductor.216 The intrinsic fundamental-gap exciton in semiconductors is a hydrogenically bound hole-electron pair, the hole being derived from the top valence band and the electron from the bottom conduction band.217 The next electron ... will go into a higher band .. .2" We will consider two separate regions: (i) energies below the top of the valence band and (ii) energies within the semiconductor forbidden band gap.2" ... the electrons fill the allowed states ... from the bottom upward, just as water fills a bottle.220 Energy bands in a semiconductor are pictured not only as vertically arranged but also as oriented with respect to the vertical and horizontal axes: A high electric field tilts the band in a semiconductor. The slope of the tilt is [formula] ... the electrons are ... driven toward the upper edge of the tilted band.221 The change of the energy of an electron is reconceptualised as a transition from one state to another, from one band to another, or within a band: Consider any simple optical transition in which an electron bound to an impurity is taken from one band to another .., 222 The acceleration of an electron in quantum mechanics is described by the electron vacating the state it initially occupied, as it simultaneously enters a different allowed state, which ... must necessarily be vacant before any occupation can occur.223 Quantum mechanically we may view the electron as being induced to enter a succession of adjacent allowed states by electric-field-induced transitions.224 In semiconductors, an increase in temperature leads to more excitation of electrons from the highest energy filled band across the gap to the adjacent empty band.225 The (literal) removal of an electron from an atom in a semiconductor and its becoming mobile is referred to in terms of a "removal" from a valence band and a transition to a conduction band: 212 213 214

215 216 217 2

ScAm, Nov. 1983: 118. ScAm, April 1984: 47. ScAm, Nov 1983: 118.

ibid. Encyclopaedia of Physical Science and Technology, 5: 295. ibid.

" Solymar and Walsh 1979: 141.

219 220

221 222 123 224 225

Solid State Physics 1977 C 10,3: 2167. ScAm, March 1984: 70. ScAm, Nov. 1983: 118. Encyclopaedia of Physical Science and Technology, 5: 302. ibid., 11:468. ibid. ibid.

127 At greater temperatures an occasional electron acquires the energy needed for it to reach the conduction band. That is, the electron becomes mobile.226 We are dealing with the Zener tunnelling from the donor band to conduction subbands.227 Oxygen will give up part of its electrons to the conduction band.228 For an intrinsic semiconductor each electron excited into the conduction band leaves a hole behind in the valence band.225 Another element in the spatialised model is the "electron hole". The concept of an electron "hole" receives a double interpretation - as a spatial relation in physical space: the absence of an electron in an atom, or else as its absence in the spatially conceived band of energy: hole:

vacancy in a normally filled energy band, either as result of an electron being elevated by thermal energy to the conduction band, so producing a hole - electron pair, or as a result of one of the crystal lattice sites being occupied by an acceptor impurity atom. Such vacancies are mobile and contribute to electric current in the same manner as positive carriers, and mathematically are equivalent to positrons.626

You may think of a hole ... as an electron missing from the top of the valence band, or as the actual physical absence of an electron from a place where it would be desirable to have one.130 Consider the description of the same process in popular scientific style: ... to jump through the forbidden band to the empty band above it ..."' ... additional energy must be provided to the electron ... if it is to climb to the conduction band.2" When a photon is absorbed by a semiconductor crystal, it promotes an electron from a filled valence band to an empty conduction band.2" The valence band and the conduction band do not overlap in energy, yet they are not very far apart. If the valence band and the conduction band would overlap, electrons from the uppermost levels of valence would 'flow' freely into lower-lying conduction-band levels.254 The electrons in a semiconductor must be transferred across the band gap.2" When an electron is removed from the valence band by a photon, it leaves an empty state behind, just as a bubble is formed when a drop is removed from a filled bottle of liquid. This empty state, or absence of an electron in the valence band, is called a hole.214 Both the electron and the hole quickly proceed to their state of minimum energy. The excited electron falls to the bottom of the conduction band, and the hole rises like a bubble in a bottle of water to the top of the valence band. The hole rises because the electrons remaining in the valence band displace the hole as if they fall into the lowest of the available states.237

226 227 228 229 m 231 232 233 234 235 236 237

ScAm, Nov. 1983: 118. Physica Status Solidi (b) 52, 1972: 537. Encyclopaedia of Physical Science and Technology, 5: 312. Solymar and Walsh 1979: 151. ibid.: 154. Beiser 1995: 354. ibid. ScAm, March 1984: 70. ScAm, Nov. 1983: 118. ScAm, Nov. 1983: 118. ScAm, March 1984: 70. ScAm, March 1984: 72.

128 ... the electron eventually drops into the hole.238 The electron will tumble downward to the lower edge of the conduction band.2"

Both renderings of the phenomena in question, in the specialists' language, and in the language of the popular scientific texts which we assume to be everyday language, are based on the band model based on underlying metaphors "CHANGE IS MOVEMENT", "MORE IS UP", and "STATE IS CONTAINER". A comparison of their wording shows that the vocabulary of the scientific language tends to be poorer in their satellite metaphors than the language of popularisers. Whereas the popularisers are less restricted in the generation of satellite metaphors derived from the same underlying metaphors, scientific texts use terminology whenever available, that is, they tend to restrict their use of satellite metaphors to the lexicalised ones. Where the specialist speaks of promoting, transition or excitation (verbs: promote, excite) from one state (band) to another, the popularisers use freely a range of verbs denoting (originally) displacement and change of extension: fall (to the bottom) tumble downward rise (like a bubble) drop into (a hole) squeeze out flow transfer across jump through climb to The specialist's language and the populariser's language reflect the process of meaning generation actualising via the band model of solids the same underlying metaphors; the difference being that in the specialist's language the process has been accomplished and has led to an established set of expressions, including defined terms, which are only sporadically accompanied by expressions generated spontaneously from the underlying spatial model; while in the populariser's language this generation of meaning is continued throughout. The above-mentioned verbs (promote, excite) are not physical terms because their meanings are not fixed by definition; they are, however, firmly established elements of the language of these branches of physics to which the band model of solids belongs, through their collocations with physical terms (electron, particle, energy etc.) which draw upon the band model with its underlying metaphors. The research in phraseology of LSP240 counts the status of such words among its open problems (cf. Picht 1989). The questions asked are, among others: What semantic changes does a verb of general language undergo, when it is applied in the LSP-context? Which factors cause these changes: the context as a whole, the particular field of application, the co-occuring agents? Is it actually the same verb if appearing in common language and in the physical text? Are we dealing with a new meaning, or a shade of meaning? Which criteria are applicable to differentiate between these two options? We suggest that such verbs might be dealt with by being characterised as general language words used technically on a metaphorical basis, instead of by retaining the exclusive charac218

ScAm, March 1984: 73. "' ScAm, Nov. 1983: 118. 240 Languages for Special Purposes.

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ter of the dichotomy between polysemy and shades of meaning. Whether this approach is actually deployable in view of the specific methods and purposes of LSP-research, we do not venture to decide. 4.2.5.7. "More is up" in the energy potential field The spatial imagery rooted in the "MORE IS UP" underlying metaphor gives rise to a system of closely related termini of quantum mechanics such as potential wall potential trough potential well potential hill potential hole quantum well potential barrier potential step In these terms, referring to the values of energy potential in the potential (energy) field on the quantum level, the denominations are imported from objects known from everyday experience, characterised by extension in space (height, depth, breadth). The properties highlighted by the metaphor - the ground of the meaning transfer - are: - spatial extension (shape), - impenetrability (under typical conditions) of their physical boundaries. Taken together, the above listed terms build a system functioning on the imagistic and the linguistic levels similar to the band model of solid. They constitute a model of the potential field spatialised in terms pertaining originally to geodetic and architectonic configurations and provide a way of speaking about the motions of particles in this field on the quantum level. For example, the passing of a particle through a region in space characterised by a strong potential field is re-conceptualised as "passing over a potential wall" (see quotations below). Another term belonging to the same system is tunnel effect, derived from the notion of a potential barrier (potential hill): if a particle is found on the other side of a potential barrier in spite of its energy being lower than that necessary to get "over" the barrier, it is said to have "tunnelled" through it. Below is the list of the component terms of this system with their technical definitions and quotations illustrating their usage. nuclear barrier= =potential barrier= = energy barrier= potential hill:

241 242

the region of high potential energy through which a charged particle must pass on leaving or entering an atomic nucleus.24' Maximum in the curve covering two regions of potential energy ... Passage of a charged particle across the boundary should be prevented unless it has energy greater than that corresponding to the barrier. Wave-mechanical considerations, however, indicate that there is a definite probability for a particle to pass through the barrier.242

Concise Dictionary of Physics. 1979. Chambers Dictionary of Science and Technology. 1976.

130 potential hole = potential well: The potential ... must be more or less constant inside the nucleus and increase sharply at the boundary, the distribution forming a 'potential hole' of the shape shown.24' There would be no energy available to take the Higgs field over the barrier.244 ... switching devices employ a potential barrier between two electrodes ... lowered to switch on the device.245 potential step:

idealized variation in electrical potential, over which all electrons in motion should pass, according to classical physics.24*

potential trough: = potential well potential wall:

a region in a field of force in which the potential increases sharply.1M

If this theory ... is correct, it is difficult to reconcile the results of Pose, who finds quite sharp resonance levels in Al. with the results of experiments on alpha particles of sufficient energy to pass over the top of the potential wall.247 The positively valued parameters A and & are to be determined to fit the binding energies of the deuteron and the alpha-particle. Evidently A and l/a/2 are directly proportional to the depth and breadth, respectively, of the potential wall.248 potential well:

a region in a field of force in which the potential is significantly lower than at points immediately outside it, so that a particle in it is likely to remain there unless it gains a relatively large amount of energy.184 A pictorial description of the region within a potential barrier in which a particle is contained unless it can 'jump' the barrier or 'tunnel' through it.405

Even very refined experiments at low energies do not suffice to determine more than an 'effective range' and 'depth' of the potential well, leaving the detailed shape completely indeterminate.249 The positive valued parameters A and a are to be determined to fit the bending particles of the deutron and the alpha-particle. Evidently A and 1/a x Ω are directly proportional to the depth and breadth, respectively, of the potential well.250 tunelling=tunnel effect:

243 244 245 246 247 248 249 250

the passage through a potential barrier of a particle whose energy is less than the barrier height. It is impossible according to classical mechanics but has a finite (but small) probability according to wave mechanics. The wave associated with the particle may be thought of as being nearly totally reflected by the barrier with a small fraction being transmitted through it.405 Piercing of a narrow potential barrier by a current carrier which cannot do so classically, but, according to wave-mechanics, has a finite probability of penetrating.401

Gamov 1931: 18. Quoted in O.E.D., 2nd edition. ScAm, May 1985:96. Einspruch 1985: 16. Hogarton 1963. Proc. R. Soc. 133, 1931:238. Physical Review 47, 1935: 852/1. Blatt and Weisskopf 1952,2: 49. Quoted in O.E.D., 2nd edition. Physical Review 47, 1935: 852/1.

131 ... a particle can tunnel through the barrier ..."' ... a quantum field fluctuation would occasionally cause the Higgs fields in a small region of space to 'tunnel' through the energy barrier."2 Correspondingly, words denoting primarily the spatial extensions have applied to the values of potential energy: energy level breadth (width):

the energy spread associated with a given energy level which, according to the uncertainty principle, is inversely proportional to the mean life of the atom, molecule, nucleus, etc. This breadth is reflected in the breadth of the spectral lines emitted in a transition between two states.405

barrier height:

a maximum energy of the potential barrier.

4.2.5.8. Double/blended recipients of metaphorical denotations: potential wall, potential well, potential barrier "More is up" seems to explain straightforwardly and satisfactorily the genesis of the terms potential wall, potential well (trough). In a potential wall, the energy potential is suddenly higher than that of its surroundings, just as a wall is higher than the neighbouring ground. In a potential well, the energy potential is suddenly lower than that of its immediate surroundings, which is also a property of a well, or trough. The analysis of the dictionary definitions of the terms potential well and potential barrier (hill) shows, however, that in the case of these terms we may speak of two different (albeit closely related) referents or recipient subjects for the transfer of meaning from the donor subjects: - the fragments of two-dimensional graphic representations (energy plotted against position), - the regions in the space surrounding an atomic nucleus characterised by certain values of the electric potential. Consider the dictionary definitions given to these terms, contradictory as far as the referent of a given expression is concerned: potential well:

the region of an energy level diagram,"3 region of an energy diagram401

versus

a region in a field of force in which the potential is significantly lower than at points immediately outside it.184 potential barrier:

the region of high potential energy through which a charged particle must pass on leaving or entering an atomic nucleus405

versus 251 252 253

Sproull 1964: 498. ScAm, May 1985: 96. Elsevier's Dictionary of Nuclear Science and Technology. 1970.

132 maximum in the curve covering two regions of potential energy ... Passage of a charged particle across the boundary should be prevented unless it has energy greater than that corresponding to the barrier. Wave-mechanical considerations, however, indicate that there is a definite probability for a particle to pass through the barrier.2"

The double reference can be accounted for as being associated with two distinct, albeit closely related, grounds for the meaning transfer: • donor situation: physical bodies in the gravitational field of the earth donor subjects: physical bodies characterised by depth, height, width recipient situation: the field of force surrounding an atomic nucleus recipient subjects: regions of this field offeree characterised by different values of energy potential In this case, regions in the field offeree are characterised as having a certain height (depth) which depends on the amount of kinetic energy a particle must have in order to reach them or the potential energy it has when placed in them. There is a physical analogy coherent with the conceptual analogy between the donor and recipient situations: both the force binding electrons and nucleons together and the gravitational force are inverse-square attractive forces; potential energy of a body (particle) in such systems is a function of the distance between the two attracting bodies. The concept of potential energy pertains to objects in the earth's gravitational field. The energy necessary for a material body to reach another point in space (the top of a wall, etc.) and, consequently, the potential energy it has when placed at this point is a function of the position of this point relative to the surface of the earth. We describe this position in terms of height or depth, properties characterising objects such as walls, hills, and wells. On the basis of the physical analogy, regions in space in sub-atomic dimensions characterised by higher values of potential energy (that is, the kinetic energy which a particle must have in order to reach or penetrate them) are, then, conceptualised as "higher" than those characterised by lower values of potential energy, which motivates the import of names from extended objects characterised by depth and height. • donor subjects: physical bodies characterised by depth, height, width recipient situation: a diagram plotting energy against position recipient subjects: fragments of the diagram The visible representation (in this case, the energy diagram) allows us to conceptualise the physical situation under study in spatial terms and reinforces our tendency to do so. Moreover, such a representation makes it possible to verbally represent the distribution of physical parameters in spatial terms. In a diagram visualising the potential energy of a charged particle dependent on the position of a particle, differences in potential energy are also rendered as differences of position on the vertical axis - potential energy is visualised as the "height" of a point above the foot of the diagram. Differences in energy values are translated into distances in space, in accordance with the underlying metaphor "more is up". 2:4

Chambers Dictionary of Science and Technology. 1976.

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The shapes of the fragments of a diagram motivate the transfer of denominations from known objects of similar shapes. There are, then, two congruent bases for the transfer of meaning leading to the terms potential well, potential wall, potential barrier: • corresponding to the target notion being a region in the field of force, there is a physical analogy: in each case we are dealing with potential energy in an inverse-square attraction system; "more is up" is a physical relation between variables (energy and position) within the donor situation; • corresponding to the target notion being a part of an energy diagram, shapes of the graphical renderings of the dependence between the potential energy and position are based on the universal "more is up" metaphor. We propose interpreting this referential ambiguity as a case of a "blended" rather than a "double" referential identity of the terms in question. This blend is a consequence of (1) the function of graphic representations, which is to transport physical phenomena into the perceptual presence of physicists, (2) the similar function of the physical analogy, modelling directly imperceptible situations after situations which are perceptually experienced. The dictionaries differ in assigning reference to these terms because their actual use in different data samples may favour one or another interpretation, but also reference-blurring alterations between the two possible referents within one text or one sentence occur in scientific reports (we suppose that they occur much more frequently in oral talks of scientists, but we have had no access to such data). They pose no interpretative difficulties as the ambiguity is physically of no consequence - the energy diagram shows energy as a function of position in the field of force, i.e. differences of position in space (e.g. surrounding an atomic nucleus) are mapped onto differences of positions on a diagram. Consider also the following quotations: Evidently A and I/a χ Ω are directly proportional to the depth and breadth, respectively, of the potential well.255 The potential wells are separated from each other by potential barriers of height Vo and width w. 254

In these quotations, "breath" and "width" are spatial dimensions. "Depth" and "height" are energy values, measured in eV. That means that the former two can be regarded as referring directly to the space in which the physical events under study take place, while the latter two refer directly to the graphic and/or conceptual representation re-construing these events in spatial terms, and only via such a figuration to the physical aspects of the situation under study. We think it would be more correct to speak in this case of "blurred" or "blended" reference than of a shift of reference from the metaphorically mediated for the expressions "depth" and "height" to the literal for the expressions "breath" and "width". 4.2.6. Periodic changes The abandonment of the aether hypothesis and its replacement with the concept of a nonmaterial field of force, which accompanied the mathematical redefinition of wave 255 256

Physical Review 47, 1935: 852/1. Solymar and Walsh 1979: 120.

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eliminating the requirement for its mechanical interpretation, amounted to a generalisation of the wave concept so that the relatively central component of its meaning - the displacement of particles of a material medium - turned to a marginal optional component. As indicated in the section on the wave concept, we interpret the meaning generalisation of the notion of "undulation" after the mechanical hypothesis had been eliminated as rooted in the ubiquitous metaphor "CHANGE=MOVEMENT". The same process of generalisation of meaning through generalisation from dislocation (change of place) to other kinds of change took place in the case of other words related to the concept of undulation (wave). Verbs which originally denoted a periodic change of position of a material particle: oscillate, vibrate, fluctuate, and nouns derived from these verbs: oscillation, vibration, fluctuation, came to denote periodic change of other physical quantities characterising a physical system, most typically of the strength of the field offeree. The Oxford English Dictionary, 2nd edition, gives the following definitions and source quotations for the lexemes in question: oscillate 1. to swing backwards and forwards, like a pendulum; to vibrate; to move to and fro between two points. 1726 Stone Mathematical Dictionary: If a single Pendulum be suspended between two semi-cycloids .. so that the string as it oscillates, folds about them, all the oscillations, however unequal, will be Isochronal in a Non-resisting Medium. 2. fig. to fluctuate between two opinions, principles, purposes, etc., each of which is held in succession; to vary between two limits which are reached alternatively. vibrate 1. of persons: to move to and fro in a fight or struggle (obs.); 2. of a pendulum, etc.: to swing to and fro; to oscillate. 1667 Philosophical Transactions II. 440. A Pendulum .. three foot, three inches .. between the middle of the Bullet and the upper end of the Thread, where it is fastened .. when it vibrates. 3. a. of sounds: to strike on, sound in, the ear, etc., with an effect like that of a vibrating chord; to resound; to continue to be heard. Chiefly poet. 4. b. spec, in physics 1774 Goldsmith Natural History (1776) II. 163. If we strike a bell, or a stretched string, for instance, .. a single blow produces a sound .. which is multiplied as often as it happens to undulate, or vibrate. 5. fig. to move or oscillate between (or betwixt) two extreme conditions, opinions, etc.; to fluctuate or vary from one extreme to another. vibration 1668 Wilkins Real Character 191. The most probable way for the affecting of this, is that which was first suggested by Doctor Christopher Wren, namely, by Vibration of a Pendulum ... 1700 Moxon Mathematical Dictionary Vibration, the Motion of a Pendulum in a Clock, which moves in the long sort of a secant in

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Time backward and forward. 1794 Sulivan View Nat., I, 168. An aether,.. rendered luminous by a vibration occasioned by the planetary motion. 5b: variation in extent, etc. 1860 Maury Phys. Geogr. Sea VI. $329. The extreme vibration of this zone is between the parallels of 17° and 38° north. fluctuate 1. to move like a wave or waves, rise and fall in or as in waves; to be tossed up and down on the waves; lit. or with conscious metaphor. 2. fig. of things, conditions, etc.: to vary irregularly, undergo alternating changes in level, position, form, constituent elements, etc. In all the quotations in the O.E.D., with the exception of those labelled as figurative, the words "vibrate", "oscillate", "fluctuate" refer to displacement of material bodies. In the process of generalisation of meaning, the semantic component "position in space" came to be replaced by other physical parameters, as illustrated in the quotations below: ... powerful sources ... whose X-ray intensity fluctuates not quite periodically.257 ... fuzzy, irregular vacuum fluctuations .. ,258 . . . the amplitude of a wave of coherent light fluctuates randomly ..."' The wave in the cavity represents oscillations of the electromagnetic field ... the strength of the electromagnetic field during one period goes from zero up to some maximum value, back to zero, down to some maximum negative value and back up to zero again.260

4.3. Animism and anthropomorphism 4.3.1. Animisms and anthropomorphisms as explanatory and articulatory devices in physical science Anthropomorphism (personification) and animism ("organification") are underlying metaphors which, at some stage, have also played a role of a world theory. The notions of animism and anthropomorphism define metaphorical donor and recipient domains very broadly, the former being the animate and the human sphere, the latter the inanimate and non-human in general. They are implemented in numerous more specific underlying metaphors relating particular pairs of closer specified domains. Reasoning and talking of inanimate entities in ways violating the semantic restriction "+animate" and of non-human entities in ways proper to human beings is a widely used means of thought and expression in common language. The language of physics shares this tendency with common language: the analysis of metaphorical denotations in physical terminology shows that the sphere of human 257 238 259 240

ScAm, Nov. 1988: 2. ScAm, May 1988: 32. ibid.: 38. ScAm, May 1988: 35.

136 and animal physiology, psychology, and sociology has, besides the denotations based on spatialisation metaphor, the highest frequency as their donor domain. Our differentiation between organifications and personifications is merely verbal. In many cases it is possible to specify whether a given concept or expression "attributes" to an inanimate entity, process, abstraction etc. specifically human features, or features of an animate being in general. In practice, however, numerous authors talk of personification where it would be seemingly sufficient to talk of animism, so that the difference becomes rather vague. Actually, we frequently interpret not only the physical but also the animal world through a projection of subjectively knowable human experience, e.g. love, like and dislike, suffering, volition, etc. upon other animate beings; that is, we use the human as an articulatory and explanatory device for the animate in general (cf. Low 1990). That is why it would not be of any advantage for our purposes to try to keep the two kinds apart, and in what follows we treat animism and anthropomorphism jointly in one breath. In the chapter on the transfer of denotations from the animate/human donor field we will also not differentiate between the violation by metaphorical expressions of the semantic restrictions "+animate, +human" on the one hand, and "+animate" on the other. On the conceptual-theoretical level, the fact that the human being and his psychical and sensomotoric experience has functioned for a long time as a basic explanatory principle for the world is manifest, for example, in the interactive analogy microcosm-macrocosm imposing a structural and functional analogy upon the human body and the cosmos, the anthropomorphic notion of force, and the explanation of hydraulic phenomena with the notion of "horror vacui", nature's abhorrence of vacuum. In the 16th century it was still a matter of course to explain physical phenomena by means of hylopsychic notions, such as "sympathy", or "friendship", and "antipathy", pertaining to attraction and repulsion phenomena. Modern science introduced a requirement that the donor domains of extended metaphors used in description and explanation ("metaphorical redescription") of natural phenomena must be restricted to the physical (other physical domains). This requirement has been fulfilled on the model-theoretical level, but not necessarily so on the meta-theoretical level: Im Allgemeinen erinnern Erklärungen mit Hilfe des Energieprinzips (das man wohl auch formulieren könnte, in dem man von dem offensichtlichen Abscheu der Natur gegen das Verlorengehen von Energie spräche) immer sehr stark an die Argumentationen, die auf dem horror vacui beruhen.2" The assumptions of what constitutes a valid physical explanation seem to have been guided until very recently by an anthropomorphic principle functioning on the meta-theoretical level, as an "absolute metaphor" in Blumenberg's sense, constituting the broadest frame for reasoning and talking about the physical world to which it was hard to conceive any alternative: early modern science defined its aim as exploring "the laws of nature" or "physical laws", these notions being evidently anthropomorphic. They render natural processes as controlled by a personified agent (nature), with which they are at the same time identical. Physical processes become personified, since creating a relation between them and the concept of the law situates them in the context of duties, obligations, prohibitions, which originated in the social - legal and moral - sphere of human existence. The extension of the notion of the law upon the non-human world provides a conceptual link between the human domain and physical phenomena: the notion of the law of nature reflects the perception of Dijksterhuis 1956: 161.

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the social order and the order of physical phenomena as parallel aspects of reality. The same underlying metaphor manifests itself in such expressions as "forbidden" or "allowed" states, transitions, zones, etc. It is conceivable that other words, such as "possible" or "impossible", could be used instead, but the items selected have been those consistent with the underlying metaphor of "law". Today, the way of speaking associated with the metaphysical assumption of a fully determined course of physical processes tends to be eliminated with the help of the notion of probability, so that the "scientific law" becomes, to a large extent, a verbal cliche dissociated from its earlier conceptual impact. Nevertheless, as Dijksterhuis' comment shows, the sphere of volition as the explanatory metaphor for regularities of nature often naturally and imperceptibly shapes the formulation of the ideas of physics. The development of human sciences such as sociology and psychology has been marked from their very beginnings in the 19th century by the aspiration to advance them to the status of "real" sciences by making their methodologies appear similar to those of exact sciences such as physics and chemistry. The crowning form of these efforts is to take over concepts from exact sciences, which have secured their claim to objective certainty thanks to pragmatic success. The relatively early emancipation of exact sciences, compared with those dealing with human beings, and their paradigmatic function as disciplines of science has been a stabilising factor for the tendency to assume that the reliable knowledge that is available to us in the first instance is the objective knowledge of nature and its regularities, in contrast to the hardly graspable complexities of the human psyche. In this way, the actual direction of the process of concept formation and acquisition of knowledge has been misconceived, and trying to point out its actual direction sounds paradoxical. The paradox can be briefly formulated as follows: the final aim of exact sciences is to gain the same degree of certainty in describing the world of nature which we have concerning that which we subjectively experience.262 Things which are accessible to us only through observation and excluded from the subjectively knowable are excluded from the sphere of certain knowledge. The only knowledge directly available to us is that of ourselves. It is through the process of transfer from ourselves to the world Out there', which we access only indirectly through observation, that we can understand the latter and lend it an intelligible structure. Personification (anthropomorphism) is the natural means of lending intelligibility to the world Out there', and when it takes the form of linguistic expressions, they are to be viewed in this context, that is, as surface manifestations of the ubiquitous extended metaphor using human cognitive, emotional, and bodily experience as an explanatory principle for the world. In what follows we sketch briefly the findings by Ochs et al. (1996) concerning how the conceptual self-projection of the cognitive subject into the physical system under study is applied in verbal communication between physicists. These findings closely link the issue of the emphatic mode of conceptualisation with the spatialised conceptual representation of physical processes, which we discussed in the preceding chapter. Further, we exemplify the role played by anthropomorphism on the conceptual and theoretical level in physics by the notion of force as the constitutive metaphor of classical mechanics. An "absolute" The history of this recognition can be traced back to Giambattista Vico, who differentiated between the knowledge of verum (true) and certum (certain); the cartesian descending order of sciences according to their truth contents, that is, geometry, arithmetics, mechanics, physics, and moral sciences constitutes the ascending order in view of the certainty resulting from the degree of their immediate familiarity to the human being. Cf. Vico, quoted in Proß 1978: 60-61.

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anthropomorphic metaphor - personification of nature - will be dealt with in section 3.3.4. Chapter 8 presents some lexicalised anthropomorphisms performing the stylistic, or rhetorical, function in the expositions of physical theory. Examples of stipulative anthropomorphisms in physical terminology will be given in section 10.4.4.3. dealing with the transfer of denotations. 4.3.2. Spatial representation and self-projection in the interpretative activity of physicists Ochs et al. (1996) offer us a close look at the interface between spatial metaphor, spatial representation, and the blurring of human/inanimate distinction in the conceptualisation of, and in the talk about, physical events. In the course of making sense of their own and others' scientific research, scientists sometimes combine talk, gesture, and graphic representation in ways that seem to blur the distinction between scientist and the physical world under scrutiny. The authors argue that in scientific interaction, grammar works together with graphic representation and gesture to construct a referential identity which is both animate and inanimate, subject and object; and that the construction of this indeterminate referential identity plays an important role in scientists' efforts to achieve mutual understanding. Public scientific texts are written in an impersonal, detached style, resulting in the outcomes of the research being presented as the "matters of fact". At the same time, in the studies of the manner in which scientists verbally portray their own or other scientists' subjective involvement in the world of physical events, it has been noticed that in everyday informal scientific discourse in laboratory interactions and in informal accounts, scientists often refer to themselves as agents in the production of scientific knowledge. Ochs et al. (1996: 3 39) state that although much has been made of the different rhetorical effects created by that discourse practice which draws attention to the scientist (physicist) as the thematic focus of an utterance and the other discourse practice which draws the attention to the object of inquiry (a physical entity or system) as a thematic focus, these two discourses actually share a common perspective. In particular, both presuppose scientist and object of inquiry as separate and distant entities, (italics in original) These two practices, though, do not exhaust the possibilities for grammatically structuring the relationship between the physicist and physics. The authors found out that scientists express their subjective involvement not only by foregrounding their role as practitioners of scientific activity, but also "more extremely by taking the perspective of (empathizing with) some object being analyzed and by involving themselves in graphic (re)enactments of physical events".263 On the basis of examples such as But as you go below the first order transition you're still in the domain structure 'n you're trying to get out of it, they came to the conclusion that in using such forms of reference with predicates that describe entities as changing location/state or as attempting to do so, scientists are not referring exclusively to themselves as scientists nor exclusively to the object of scientific concern but rather to conflation of both ... when they use a particular set of linguistic resources, namely, constructions consisting of personal pronominal subjects (especially T and 'you') and predicates of motion/change of state (e.g. 'go', 'break up').264 263 264

Ochsetal. 1996:330. ibid.

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The observations concerning the way in which, in informal discussions, physicists grammatically construct physical entities (e.g., an atomic system) as moving through space are consistent with what we said on that subject in the preceding chapter. Further quotations illustrate how "physicists also grammatically construct physical entities as experiencers, by selecting predicates of sentience and understanding": "This system has no knowledge ofthat system"; "The system can never have time to experience those random fields". The central issue in the article, however, is neither spatialisation nor pure anthropomorphising of a physical system. It is the authors' discovery that in addition to the varied grammatical realisations of physicist and physics as distinct entities, their data are full of utterances which encode an indeterminate referent... That is, the referent constructed in these utterances appears to be neither exclusively the physicist nor the object of inquiry but rather a blended identity that blurs the distinction between the two ... Nevertheless, they appear to be completely unproblematic for the physicist interlocutors. Indeed, no one ever stops an interaction to ask, 'What do you mean 'I'm in the domain state'?' or 'How could you possibly 'go below in temperature'?'2" The sense of indeterminacy is conveyed in that the pronominal subjects (I, you) do not appear to be restricted to the speaker or the addressee, but rather to a class of referents who may participate in the events referred to in the predication, and in an animate referent being presupposed by the pronominal subject while, at the same time, the predicate seems to be attributable to an inanimate referent only (i.e., the physical object under consideration). Strips of verbal and gestural interaction are presented in which interlocutors switch among physicist-centred, physics-centred, and indeterminate perspectives within and across turns. The basis for assigning meaning extend beyond the verbal utterance, to the accompanying referential gestural practices, which are integral to collaboratively interpreting graphic representations. The authors' interpretation of their results as evidences of a "blurred identity" of the referent acknowledges that referential ambiguity is a necessary poetics of mundane scientific problem-solving in that by using indeterminate constructions as a linguistic heuristic, scientists constitute an empathy with entities they are struggling to understand. Such a referential poetics allows interlocutors to symbolically participate in events from the perspective of entities in worlds no physicist could otherwise experience ... The referent indexed by the pronoun ... travels through temperature and magnetization conditions, crosses phase transition boundaries, and experiences the effects of these changes ... Referential displacement of this sort seems especially suited to the scientist's efforts to think through physical problems ... Support for this interpretative strategy also comes from mythic accounts of scientists' flashes of insight concerning physical phenomena.. .2M (a reference to Einstein follows, cf. the section on "travelling light"). Similarly to what we observed in the case of the referential ambiguity of terms like "potential well", "potential barrier", the constructed realms in which scientists take such "interpretative journeys" are two-fold: they consist of a blend of (1) the (re)constructed world of physical events and (2) the world of visual representations of these events. Graphic displays

265 266

ibid.: 339-340. ibid.: 348-349.

140 provide physicists with a cognitive and spatial domain to inhabit and wander in. They also transport physical phenomena into the perceptual presence of physicists and serve as a locus in which physicist and physical phenomenon can be brought into physical and symbolic contact with one another... 267 The meaning of 'If I come this way' is thus built simultaneously from (1) the sensi-motor action involving Ron's fingers and hand on the blackboard and within the graphically defined space, and (2) from the symbolic meanings which have already been assigned to the marks, lines, and areas of the conventionalized graphic representation in this and previous interactions. Moreover, indexical gestures are so much a part of the physicists' discourse practices, it appears that physicists come to their understandings and interpretations of physics partly through such sensori-motoric and symbolic re-enactments of physical events and that the collaborative thinking-through process requires that this sensori-motoric involvement be witnessed and evaluated by others present.268 The conclusion is that indeterminate constructions draw interlocutors into an intersection of multiple worlds, including the world of here-and-now interaction, the world of graphic space, and the world of physical events symbolically represented by the graphic display. It is as if interlocutors are able to situate themselves simultaneously on three referential planes through their talk of this multi-levelled distribution of attention: physicists (1) attend to people and objects (especially graphic displays) in their meeting room, (2) carry out symbolic gestural motions within graphic representations, and, facilitated by these graphic representations and their own gestural enactments, (3) imagine themselves as physical systems in different physical states.2" Summing up, the authors have shown how two figurative strategies co-operate in the act of collaborative discussing of experiments: (1) a referential displacement of the identity of the physicist onto the identity of the physical entity or event, (2) gestural practices and graphic representations. Thus, indeterminate constructions provided by (1) can be understood as literal predications about physicists in the here-and-now world of the interaction who gesturally locate themselves in the world of graphic representation. At the same time, because the world of graphic representations indexes a world of physical events, these same utterances can be understood referring to physical entities experiencing the physical events represented by the graph. That graphic representations mediate between scientists and the physical entities they are struggling to understand is old hat to scholars of scientific practice. What is not old hat or obvious, however, is that graphic representations can referentially constitute scientists and physical entities as simultaneous, co-existing participants in events.™ Ochs et al. (1996) offer us a close look at how a physicist projects him - or herself onto a physical entity and into the world of physical events, reconstructed conceptually in the form of a spatial image, in order to be able to use human cognitive and bodily experience as a guide in interpreting physics. We think that this process is symmetrical to these processes in which inanimate subjects are treated, conceptually and verbally, as though they were subjects of such experience. "Anthropomorphism" is the name attached to the latter. The former has been taken much less notice of, and has not yet been assigned a name. Together they form a (nameless) category of conceptual and verbal processes in which the boundary between human and inanimate is obliterated: human subjects can experience the processes concerning 267 268 269 270

ibid.: 350. ibid.: 352-353. ibid.: 356. ibid.: 358-359.

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e.g. astrophysical or atomic systems, and the systems in question can be "experiencers" of these processes.271 The obliteration of the boundary, realised in such a two-fold way, is the ubiquitous underlying metaphor using human cognitive, emotional, and bodily experience as an explanatory principle for the world. We said before that the final aim of exact sciences is to gain the same degree of certainty in describing the world of nature which we have concerning that which we subjectively experience, and that things which are accessible to us only through observation and excluded from the subjectively knowable are excluded from the sphere of certain knowledge because the only knowledge directly available to us is that of ourselves. We think that through the transfer of themselves to the world Out there', which they access only indirectly through observation of instruments, the scientists involved in an act of interpretation are searching to simulate a psychological condition of "certain knowledge". Such a simulation is particularly tempting where there is a large amount of instrumental and theoretical mediation between the physical situation under study and the scientist, in which it is not clear what has been observed. This mediation invalidates the other way to construing the sense of cognitive certainty: the Cartesian "objectivity", which is the official choice of the modern Western science. In contrast to the cognitive identification with the object under study characteristic of animist-occultist science of the Renaissance (cf. section 5.3.1.2.), in the original Cartesian ideal, well suited to the relatively direct observation in the middle (or close to middle) dimensions, science used to be all about the observation of facts (constituted by figure and motion) by an uninvolved observer. Today, the ideal (minus the restriction of "facts" to facts concerning figure and motion) leads further existence in the practices of physicists: the traces of emphatic involvement are erased in official texts, where the objective perspective is required. 4.3.3. The concept of force: Newtonian mechanics The concept of force, the foundation of classical mechanics which was the crowning achievement of the scientific revolution of the 17th and 18th centuries, is the most widely acknowledged example of anthropomorphism functioning on the conceptual and theoretical level in physics. Its metaphorical origin was already recognised and frequently pointed out at the time immediately following the publication of Newton's "Principia". Even if frequently questioned as non-scientific at that early period, it soon became universally accepted as a cornerstone of mechanics, so that today it is hard to imagine what turn physical science might have taken without Newton's formulation of his laws of motion, in which the concept offeree was an indispensable formal component. The incorporation of mechanical force into the basic structure of physics is generally regarded as the beginning of modern physical science, which replaced the essentially geometrico-kinematic concepts of the Aristotelian and Ptolemaic tradition. In the 19th century the non-vanishing vexing consciousness of the metaphorical character of the notion of force resulted in such reformulations of mechanical

Projecting yourself out in order to understand actions which are not yours is conceptually very close to attributing a similarity to yourself to other agents (such a projection helps you understand their actions only on the assumption that the similarity exists). What's different in these cases is an emotive stance, or distance, towards what happens - to imagine you are X, vs. to imagine X is like you - the former being a closer identification.

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theory in which it no longer served to define other physical notions; it was purified from all animistic connotations by being redefined in an operationalist manner as a derived measure, the time rate of change of momentum. But the level of conceptual and mathematical sophistication which made it possible was achieved via the earlier stages of the mechanical theory, the stages in which the notion of force played a constitutive role. In what follows we demonstrate the metaphorical, anthropomorphic origins of the physical notion of force, and briefly sketch the history of its continued criticism. In everyday language from which it entered the terminology of physics, force denotes the ability to produce the effects of push and pull (or resistance to them) by means of bodily action, and, in an extended sense, the ability to produce effects (changes) in the environment in general. The experience of the bodily strain as a causal factor leads to the formation of the concept offeree closely akin to that of a cause, or causal ability, as in O.E.D.: Force 16 1639 Fuller Holy War IVXII. (1940) 188 Two hundred and fourty Gentlemen of note died by force of the infection. Lakoffand Johnson (1980: 75) assert that "the concept of causation is based on the prototype of direct manipulation, which emerges directly from our experience". As the direct experience of manipulation involves the experience of using force, the notion of force became extended (metaphorically transferred) to other kinds of causation, transferred from bodily sensation into cause and effect situations excluded from sensomotoric experience but available to other kinds of observation. Taken originally in analogy to muscular effort and projected upon human will-power and spiritual influence, the notion of force has been projected onto inanimate things. At the same time, the experience of volition as involved in both immediate bodily causation and less direct forms of influence upon one's environment led to the association of force with the phenomena of volition in general, making it into an element of the spiritual as well as the physical aspect of reality. The concept, which originated as a projection from bodily experience upon the domain of the "less known", provided the solid foundations on which classical mechanics could develop, providing a way to explain all the changes of motion which bodies experience, and guidance concerning how to think about physical phenomena. The concept of force abstracted from the direct experience of bodily strain has a long history prior to its inception in the conceptual system of classical mechanics. According to Jammer (1957), it was present in the conceptual systems of all ancient civilisations, and stood in close relation to religious ideas. The belief in occult powers, expressing the panpsychism of early stages of human civilisation, preserved for us in the familiar expression "forces of nature", gave rise to the personification of "force" into deity. Numerous religions accomodate the concept of "divine force" as a basic attribute of personal deity. Ancient mythology (the 'physics' of the pre-scientific stage, as Jammer calls it) considered anthropomorphically conceived powers, or forces, as causal agents in natural and historical processes; for a long time, also during the Enlightment, they continued their existence in the occult study of nature, in the pursuit of the "active principles" acting as agents in material bodies. In the Middle Ages, it is a fundamental assumption of philosophy that divine intelligence is

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the motive force of celestial bodies.272 The forces of nature are the manifestation of divine power and the intermediaries between God and the physical universe. The concept of force in classical mechanics developed out of this pre-scientific notion of force, or forces, as agents in natural phenomena, which however lacked all quantitative and physical determination. In early modern physical science, the concept of force retained some of its vitalistic and volitional connotations, which made it subject to attacks after being elevated to the position of a fundamental notion of mechanics. The panpsychic, spiritual character of the concept of force at the advent of modern science is clearly revealed in Copernicus' (1543, 1965, Book 1, Chpt. 9) comment on gravity as a certain natural appetition given to the part of the earth by divine providence ... in order that they may be restored to their unity and to their integrity by reuniting in the shape of a sphere. In a similar vein, William Gilbert (1600, 1952: 12) exposes the psychic character of the notion of attractive forces saying: Cut the stone in two equal parts ... You will find that a, the north point, will turn to the south as before ... But b and c, before connected, now separated from each other, are not what they were before; b is now south while c is north, b attracts c, longing for union and restoration of the original continuity ... [...JNature will not suffer an unjust and inequitable peace ... but makes war and employs force to make bodies asquiesce fairly and justly ... [...JBoth stones, the weaker and the stronger ... with all their might tend to union ... The parts nigher the pole ... have greater attractive force; and ... in the pole itself shall be the seat, the throne as it were, of a high and splendid power ... magnetic bodies brought near shall be attracted most powerfully and relinquished with most reluctance. So, too, the poles are readiest to spurn and drive away what is presented to them amiss, and what is uncomfortable and foreign. He also speaks of "friendship" (or "sympathy") of iron for the lodestone. Elsewhere, we read: Everything terrestrial is united to the earth; similarly, everything homogeneous with the sun tends towards the sun, all that is lunar toward the moon and the same applies to other bodies constituting the universe ... It is not a question of an appetite which brings the parts towards a certain place ... but of a propensity toward the body, toward a common source, toward the mother where they were begotten, toward their origin, in which all these parts will be united and preserved and in which they will remain at rest, safe from every peril.2" These comments expose a basic feature of pre-Keplerian thought, which is the lack of clear category boundaries between psychic and physical notions. Numerous expressions used at various times by other authors for the description of gravity similarly display the merger of the spiritual and the physical prior to the establishment of the Keplerian-Newtonian system: "love" (philotes, philia) and "strife" ("neikos" ) in Empedocles, Plato's notion of "kindred elements" and life and soul as the origins of all motion,274 Copernicus' "appetentia ", "un desir naturel" of Pascal and Roberval,275 "sympathy" in various classical authors as well as 272

273 274 275

This conception developed from such earlier ideas as the Platonic idea of a world-soul, the Aristotelian doctrine of motion applied to celestial bodies, the Neo-Platonic conception of allpervading force, and religious interpretation of cosmic forces in the Jewish-Alexandrian school of thought. Cf. Jammer 1957. Gilbert 1651: 115. Quoted in Jammer 1957: 79. Plato: Timaeus. 1937, 2: 42-43. Pascal and Roberval 1636, 1894. Quoted in Jammer 1957:

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Hieronymo Fracastoro,276 "intelligentiae assistences" and "spiritus rector" in Aquinas, "spiritus motrix" in Nicolaus of Cusa,277 "convenientia" and "disconvenientia" and "friendly relation" in Ludovicus,278 "affectio corporea, mutua inter cognata corpora", "anima", and "facultate animali" in Kepler, "intelligentiae motrix" in Scaliger.279 The mature stage in the development of the concept of force begins with the attempts at its quantitative determination. A notable step towards the mathematical definition of force was made by Johannes Kepler. His success in establishing mathematical dependencies between the velocities of planets and their distance from the sun led him to the conclusion that the force governing their motions belongs to the material aspects of reality. Although in Kepler's works the conception of gravitational attraction is intermingled with spiritual elements of expression, such as "anima motrix", "species immateriata", and "facultate animali", it may be supposed that he employs such language simply because he is not as yet in possession of other expressions free from psychic connotations. In "Mysterium cosmographicum" (1596) Kepler refers to force as a soul (anima), but at the same time treats it as a physical quantity (cf. Jammer 1957: 82). In the second edition of this work, Kepler explicitly rejects "psychism" and introduces for the first time an opposition between the soul (anima) as a spiritual notion and a force (vis) as belonging to material, non-spirited aspects of reality. This dissociation of force and soul marks the newly emerging separation of the physical and spiritual domains: If you substitute for the word soul the word 'force', you have the very principle on which the celestial physics of the treatise on Mars etc. is based ... Formerly I believed that the cause of planetary motion is a soul... But when I realised that these motive causes alternate with the distance from the sun, I came to the conclusion that this force is something corporeal, if not so properly, at least in a certain sense .. .28° With Kepler's work, physical force becomes stripped of psychic connotations and dissociated from the phenomena of volition as well as supernatural causation. Descartes conceived "force" as a merely fictitious appearance. His world consists of pure matter and pure spirit only, where there is no place for mechanico-psychic notions such as force. Matter has to be cleared of all spiritual constituents, "inherent forms" or "tendencies", to which the notion of force belongs. For him, the notion of force as an agent causing gravity, implying action at a distance, would amount to attributing intelligence to material particles, as though they could be aware of what happens elsewhere. In his kinematic mechanics there is no place for force and action at a distance. In contrast to this, Isaac Newton (1729, 1934, Book 1: 7) makes "forces ... propagated through the spaces round about" into a principal concept of mechanics. Historians have traced his concept of force back to its sources in the occult sciences. From our linguistic stance, it is the common language basis of the self-evident, self-explanatory character of his "force" that is of main interest. The basic form in which forces manifest themselves is attraction. His analysis of gravitational phenomena is conceived in terms such as "bodies attracting each other"; "the attractions of one corpuscle towards the several particles of one sphere"; "mutual attraction". 276 217 278 279 280

Fracastoro 1546. Quoted ibid. Quoted ibid. Ludovicus 1540, lib. II. Quoted ibid. Scaliger 1557. Quoted ibid. Kepler, quoted ibid.: 90.

145 Opinions are divided on the question as to whether such formulations carry with them, as well, an ontological commitment on Newton's part. His stand towards them could have changed once or twice during his lifetime (cf. Home 1992). Westfall (1980) argues that Newton, inspired by the alchemistic notion of the existence of active principles in matter, believed that the forces had a real existence of their own as true action at a distance, and were in no need of mechanical explanations. The other view is that in Newton's works, these expressions are to be taken phenomenologically, that is, metaphorically. They do not attribute causal powers to matter, and they do not express a belief in action at a distance as they also co-occur with Newton's attempts to explain gravity mechanically, through the aether hypothesis.281 What he means by attraction is merely "the tendency of bodies to approach each other", that is, the phenomenon of bodies coming closer to each other when certain conditions are met, and the mathematical description of this motion. However, in his attempt to formulate the principles of mechanical phenomena, he sees himself confronted with the difficulty of using language which would be free from any trace of anthropomorphism, ascribing to bodies "tendencies", "endeavours", being "endowed with powers", etc.. The expressions he finds himself forced to use are unavoidably loaded with the connotation of an active role played by bodies, and of the forces involved as innate in matter. This view seems to find support in Newton's linguistic awareness expressed in the frequent hedging and disambiguating of his expressions. Realising that his vocabulary may be misleading as it can be interpreted as attributing the role of active agents in gravitation to the material bodies, he asserts his opposite intention in this respect: I here design only to give a mathematical notion of those forces, without considering their physical causes and seats.282 I ... use the words attraction, impulse, or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically; wherefore the reader is not to imagine that by those words I anywhere take upon me to decide the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only mathematical points); when at any time I happen to speak of these centres as attracting, or as endued with attractive powers.2*4 [...]! here use the word attraction in general for any endavour, of what kind soever, made by bodies to approach to each other; whether that endavour arise from the action of the bodies themselves as tending mutually to, or agitating each other by spirits emitted; or whether it arises from the action of the aether or of the air, or of any medium whatsoever, whether corporeal or incorporeal, and how impelling bodies placed therein towards each other.285 I use the word >attraction< here to signify in general any Force by which Bodies tend towards one another, whatsoever be the Cause.284

281 282 283 284 285 286

E.g. in a letter to Boyle, Feb. 28, 1678. Newton, Principles, 1729, 1934, Book 1: 8. To deal with phenomena mathematically was to describe them by quantity, whereas physics was concerned with qualities, "natural causes" and the "essential natures" of things. Newton, Principles, 1729, 1934: 8-9. ibid.: 262. Scholium following Proposition LXIX. Newton: Opticks, 1717, 1952: 531. Query 31.

146 It is notable that whereas there is much explicit hedging to be found in his formulations as far as the notion of "attraction" is concerned, "force" (vis) itself seems to present less linguistic controversy and not to require such an amount of justification. In fact, in the last sentence, "attraction" is hedged and explained by being called a "Force", the latter used not quite synonymously with "cause", which also appears in the same sentence: here, the word "force" acts as an intermediary between "attraction" and "cause". Verbalisations such as this one support the thesis of Jammer (1957): Newton was far from regarding "force" and "attraction" as the cause of gravitational motion incapable of further analysis, and the ultimate basic level of physical explanation; at the same time, he was able to conceive and apply the notion of force as an independent, separate concept in its own right abstracted from the question of the immediate physical mechanism behind it, which followed from the fact that force, for Newton, was a concept given a priori, intuitively, and ultimately in analogy to human muscular force. a7 This claim is motivated mainly by the position of force in the Newtonian system. Modern writers sometimes interpret the second law of classical mechanics as a definition offeree;288 however, Newton clearly distinguished between definitions and laws of motion, and placing the statement about the effects of the motive force among laws rather than among definitions suggests that he considered force as a "known", that is, an aspect of reality conceivable independently of the other notion (change of motion) appearing in the same law. Reformulating Jammer by using notions we applied before to speak of some other facets of anthropomorphism, we can say that it is through imaginative self-projection of the conceiving subject upon the physical object under study that the notion of force becomes intuitively understandable. We can easily imagine ourselves in the position of a physical body upon which a force is exercised, experiencing it senso-motorically as a countering of our muscular force. Newton's contemporaries were far from unequivocal acceptance of this intuitive notion of force. Viewed from the post-Keplerian perspective distinguishing clearly between the physical and the spiritual, the metaphorical character of the concept was already recognised in the time immediately following the publication of "Principia". New science was marked by an attempt to eliminate psychic notions, as "occult properties", from the description of physical facts, and the introduction of "force" as a primitive, unexplained basic concept seemed to endanger the very fundamentals of this disciplined approach. This recognition went hand in hand with the criticism, notably by Berkeley and Hume, of the idea of causality, which for them was illegitimate in science. The most thorough contemporary criticism of the Newtonian concept of force was provided by Berkeley, in his works dealing with the philosophy of physical science. His immediate objective is to point out the illegitimacy in the use of certain general abstract notions in science, including force as a fundamental notion of Newton's dynamics. Berkeley stresses repeatedly that the expression "force" is only a way of expressing the truth that movements of material bodies (particles) proceed not chaotically, but in accordance with

287 288

Jammer 1957: 124. A view opposed e.g. by Hesse 1962. "The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed." Newton: Principia, 1725-6, 1952: 14.

147 certain laws, or regularities. He recognises the secondary, derived and fictional character of the notion of force: Nor are we concerned at all about the forces, neither can we know or measure them otherwise than by their effects, that is to say, the motions; which motions only, and not the forces, are indeed in bodies ... We are not therefore to suppose, with certain mechanic philosophers, that the minute particles of bodies have real forces or powers, by which they act on each other, to produce the various phenomena in nature. The minute corpuscles are impelled and directed, that is to say, moved to and from each other, according to various rules or laws of motion ...289 On another occasion he asserts that Force, gravity, attraction and similar terms are convenient for purposes of reasoning and for computations of motion and of moving bodies, but not for the understanding of the nature of the motion itself.290 His criticism is directed against attributing the status of physical reality ("being a true physical quality") to force, that is, being a part of "nature itself". It should not be assumed that bodies contain or exert "forces" through which they act upon each other. To introduce the term "force" as an explanatory factor into physical science is to develop a misleading vocabulary. Berkeley recognises that the origin of the notion of "force" is the human tendency to generalise the immediate sensual experience, to project it onto other domains and to attribute causation to ideas provided by this projection: When we perceive certain ideas of sense, constantly followed by other ideas, and we know that it is not of our own doing, we forthwith attribute power and agency to the ideas themselves.291 He reduces the notions of push and pull (attraction and repulsion) to purely operational status: the physicist observes a succession of sense data, connected by rules, and interprets that which precedes in their order as the cause and that which follows as the effect. It is in this sense that we say that one body is the cause of the motion of another, or impresses motion on it, pulls or pushes it: Solicitation, and striving or effort really refer only to beings that have life. When they are applied to other things they must be taken metaphorically. But philosophers should avoid metaphors. That these words have no clear and distinct meaning when not referring to either animal sensibility or the motion of the body will be plain to anyone who considers the subject seriously. [.. .JForce also is attributed to bodies. The term is used however as if it meant a quality that is known, yet is not motion, shape or any other sensible object, nor a feature of animal sensibility; which a little inspection will show to be nothing but an occult quality. Animal effort and bodily motion are commonly regarded as concomitants of this occult quality.2'2 In "Siris", he warns: Although a mechanical or mathematical philosopher may speak of ... force as existing in bodies, causing such motion and proportional thereto; yet what these forces are, which are supposed to be lodged in bodies, to be impressed on bodies, to be multiplied, divided, or communicated from one body to another, and which seem to animate bodies like abstract spirits, or souls, hath been found very difficult, not to say impossible, for thinking men to conceive and explain.2'3 289 290 291 292 293

Berkeley: Siris, 1744, sec. 234-235. 1901,3: 233-234. Berkeley: De motu, 1721, 1901,1: 506. Berkeley: A treatise concerning the principles of human knowledge, 1710, Sec. 32. 1901,1: 274. Berkeley: De motu, 1952: 203-204. Berkeley: Siris, 1901,3:241.

148 Even if we apply the terms such as force, repulsion, and attraction in a customary way, we should keep in mind their fictitious character: The word attraction and repulsion may, in compliance with custom, be used where, accurately speaking, motion alone is meant... [.. .]When ... force, power, virtue, or action is mentioned as subsisting in an extended and corporeal or mechanical being, this is not to be taken in a true, genuine, and real, but only in a gross and popular sense; which sticks in appearances, and doth not analyse things to their first principles. In compliance with established language and the use of the world, we must employ the popular current phrase. But then in regard to truth we ought to distinguish its meaning.294 To prevent the reader from losing the awareness of the metaphorical, or "inaccurate", character of these notions, Berkeley repeatedly hedges his own use of them with reformulations in terms of movements alone: It is not improbable... that... where attracting forces cease there repelling forces begin; or, to express it more properly, where bodies cease to be moved towards, they begin to be moved from each other .,. 295 (emphasis HP) ... agitated by different powers, or, to speak more accurately, moved by different laws ...296 (emphasis HP) In his comment on Newton, he says: He may perhaps sometimes be thought to forget himself, in his manner of speaking of physical agents, which in a strict sense are none at all; and in supposing real forces to exist in bodies, in which, to speak truly, attraction and repulsion should be considered as tendencies or motions, that is, as mere effects, and their laws as laws of motion.297 On the same grounds, the notion of force has been criticised by Maupertuis (1756, 1974,1: 29-30) who pointed out its metaphorical character saying: The word 'force' in its proper sense expresses a certain feeling which we experience when we wish to move a body which was at rest or to change or stop a body which was in motion. The perception which we than experience is so constantly accompanied by a change in the rest or movement of the body that we are unable to prevent ourselves from believing that it is the cause of this change. When therefore we see some change taking place in the rest or movement of a body we do not fail to say it is the effect of some force. And if we have no feeling of any effort made by us to contribute to this change and if we can only see some other bodies to which we can attribute this phenomenon, we place the force in them, as though it belonged to them. Maupertuis was also the first to recognise explicitly Newton's second law of motion, regarded by Newton as an important law of nature, as a definition of force, or a tautology298. For Maupertuis as for Berkeley, the connotation of "solicitation of striving or effort" is part and parcel of the notion of force; this constitutes the metaphorical, or "inaccurate", character of this notion when applied to inanimate bodies. 294 295 296 297 298

ibid.: 237. ibid.: 234. ibid.: 236. ibid.: 240. The tautological character of the concept lies in the fact that forces can only be recognised through their effects - acceleration of physical bodies, while, at the same time, Newton's second law declared acceleration to be an effect of applied force and proportional to it.

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In view of the mass of criticism which it encountered, the overwhelming success and the long endurance of "force" in mechanics as a basic concept could come as surprise. We think that, the advantages of its mathematical formulation notwithstanding, a large portion of the success and the endurance derives from its intuitive graspability in an alliance with the common language expression, the graspability which was the same at its origin as it is today for a novice student for the first time confronted with the concepts of classical mechanics. The effortful re-formulation by Berkeley of his original expressions in a force-free language shows how natural it has been to speak, and think of, a force. Contrary to Berkeley and Maupertuis, some half a century later, Euler (1769, letter 50; 1986: 56) comments on the term "force" in its generalised meaning freed from "animal sensibility" and muscular effort: Man hat Grund, die Schwere der Körper eine Kraft zu nennen, weil alles, was vermögend ist, einen Körper in Bewegung zu setzen, Kraft genannt wird.

Here, identifying "force" (in accordance with Newton's second law) with the cause of movement, devoid of any connotation of bodily effort, Euler actualises and sanctions the meaning which arose by metaphorical projection, affirming its status as the proper definition of the term in question. Although generally accepted in the formulation of classical mechanics, the notion offeree continued to provoke vehement objections of philosophers in the last century as well. Du Bois-Reymond (1848, XL-XLI) wrote: Die Kraft ... ist nichts als eine versteckte Ausgeburt des unwiderstehlichen Hanges zur Personifikation, der uns eingeprägt ist, gleichsam ein rhetorischer Kunstgriff unseres Gehirns, das zur tropischen Wendungen greift, weil ihm zum reinen Ausdruck die Klarheit der Vorstellung fehlt ... Was ist gewonnen, wenn man sagt, es sei die gegenseitige Anziehungskraft, wodurch zwei Stofftheilchen sich einander nähern? Nicht der Schatten einer Einsicht in das Wesen des Vorganges. Aber, seltsam genug, es liegt, für das uns innewohnende Trachten nach den Ursachen, eine Art von Beruhigung in dem unwillkürlich von unserem inneren Auge sich hinzeichnenden einer Hand, welche die träge Materie leise vor sich herschiebt, oder von unsichtbaren Polypenarmen, womit die Stofftheilchen sich umklammern, sich gegenseitig an sich zu reißen suchen, endlich in einen Knoten sich verstricken.

Karl Pearson (1892, 1951: 104) commented on the notion offeree: Primitive people attribute all motion to some will behind the moving body; for their first conception of the cause of motion lies in their own will. Thus they consider the sun as carried round by a sungod, the moon by a moon-god, while rivers flow, trees grow, and winds blow owing to the will of the various spirits which dwell within them. Slowly, scientific description replaces spiritualistic explanation. The idea, however, of enforcement, of some necessity in the order of a sequence, remains deeply rooted in man's mind, as a fossil from the spiritualistic explanation which sees in will the cause of motion;

and William James (1920: 213) asserted that If we aspire to strip off from Nature all anthropomorphic qualities, there is none we should get rid of quicker than its 'Force'.

For Mauthner, who presented large passages of his main work on the subject of metaphor in the concept formation of natural sciences, the metaphorical character of the Newtonian

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system lay not only in the notion of "force" but, even more fundamentally, in the extension of the notion of heaviness (Schwere) to the celestial bodies: Seit Menschengedanken verstand man unter dem Gewicht ungefähr den Druck des Körpers auf seine Unterlage, was wieder nur ein Bild war von dem Drucke eines Körpers auf die menschliche Hand ... Mit einem anderen Bilde stellte man sich vor, die Erde ziehe die fallenden oder schweren Körper an. Nur traten plötzlich Weltkörper in den Bereich der irdischen Anziehungskraft ...2W Mauthner implicitly defines metaphor as an extension of a concept born of immediate experience to phenomena excluded from the possibility of such an experience. According to his interpretation, even the term "weight" applied to air is a case of metaphorical speech because the attribute of air designated by this name entsprach nicht dem natürlichen Sinneneindruck eines Gewichtes in der menschlichen Hand.'00 With respect to Newtonian mechanics, Mauthner (1913: 544) speaks of "personification" of the fall or gravity; what he means is the grammatical recategorisation of the verb "to fall" into a noun ("fall") and the adjective "gravis" into a noun ("gravity") and a verb ("gravitate", German "gravitieren"). Instead of an explanation, Mauthner says, we are presented with a metaphorical redescription. The notions of gravitation and attraction have no explanatory value: Es hängt vollkommen von der metaphorischen Phantasie des Beobachters ab, ob er die geheimnisvolle Kraft in die Attraktion oder in die Gravitation hineinversetzen will, wie es von seiner Phantasie abhing, ob der Fall die Ursache der Schwere war oder umgekehrt... Alle diese Vorstellungen gehen schließlich auf den Sinneseindruck eines die Menschenhand wuchtig belastenden Körper zurück.301 The end of the 19th century witnessed attempts to eliminate the concept of force from science. Like Berkeley before them, physicists such as Barre de Saint-Venant, Lazare Carnot, Heinrich Hertz stressed that whatever problem of mechanics we consider, the forces never appear among the data or in the answer to a problem, the answers being ultimately stated solely in terms of distances, times, and velocities; thus, forces are just auxiliary props with which calculations (and thinking) may be done. For Hertz, the forces used in mechanics are just "sleeping partners"; their application to account for the observable facts is not necessary; force is not an object of direct perception, but an aid to calculation which disappears in the final solutions. Saint-Venant expressed his hope that one day physics would get rid of such occult or metaphorical notions and would solve its problems only by applying laws based on velocities and their changes. This programme was carried out at the end of the 19th century, when theories of mechanics applied the notion of force as an operationally defined derived concept utterly devoid of any anthropological, metaphysical, temporal, causal, or ideological implications. In the conceptions of Ernst Mach, Gustav Kirchoff, Heinrich Hertz, W.K. Clifford and Karl Pearson, force is reduced to purely mathematical expressions relating certain measurements of space and time. With the works of these scholars, the elimination of force as a basic concept of mechanics has been accomplished. Before these changes came, the notion of force was used to define other concepts such as the concept of work, which, in turn, was the underlying basis for the later concept of energy. "Work" (itself of metaphorical origin) was originally defined in terms of movement against w 500 501

Mauthner 1913: 543. ibid.: 540. ibid.: 544.

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resisting forces. The concept of energy originated as an abstraction from work, and referred, most broadly, to the capacity to do work. The order of "basicness" of these three concepts has become reversed in the current paradigm. Energy is today a basic physical concept which may be used to define force as an auxiliary, derived physical value. The eventual elimination of force from the level of basic concepts was a due consequence of the recognition, resulting not from a sudden discovery of difference but present from the beginning in the background of its application, that the way in which the notion of force related to experience relied upon the merge of physical and psycho-physiological domains. 4.3.4. Anthropomorphism and meta-theory: the secrets of nature and associated concepts In this section we shall deal with some meta-theoretical and methodological facets of personification: we shall have a look at the personification of nature and the associated metaphorical representations of scientific activity. A whole series of metaphors for nature and scientific research interacting with each other are around at the time modern science begins to take shape. The following are some of the interconnected concepts used to conceptualise nature and human knowledge of it: • secrets of nature; • nature as a female; • science as a hunt; • science as conquest; • nature as the New World. The common feature of all these metaphorical conceptualisations is that nature is rendered in them as an opponent of the (male) scientist, having purposes of its own in conflict with the latter's goals. The effect of this kind of conceptualisation upon the approach to the research of natural phenomena was that it mobilised the scientist to take an active, offensive attitude towards nature, which in practice meant that experiment became the essential means of insight, to be preferred to speculation in the ancient mode. In what follows, we demonstrate that all these seemingly figurative metaphors played an important role in structuring the modern attitude to doing natural science. The focus of our interest is the anthropomorphic metaphor of the secrets of nature; the remaining ones will be considered briefly with regard to the support they provide for the same turn of thought, reinforcing each other and summing up in their impact. 4.3.4.1. The secrets of nature Effort in making science It is a rather recent, but already widely acknowledged recognition that, far from being a figure of rhetoric, the notion of secrecy, constantly reappearing in the philosophical writings of the 17th century, had wide epistemological and methodological implications. Hutchinson (1982: 245-246) wrote: Because it has become a hackneyed metaphor, the intellectual advance it represents is often unappreciated, but the Scientific Revolution, with its emphasis on thoroughness and active experimentation in place of uncritical passive observation, depended on such a recognition.

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This insight goes hand in hand with contemporary view of metaphor, following Black's recognition that the metaphorical conceptualisations organise and transform the view of their recipient subject by evoking associations with the donor subject: To speak of the 'secrets of nature' is to transfer an entire system of commonplaces associated with concealment, privacy, exclusiveness, and clandestine activity onto the concept of nature. The metaphor thus organizes our view of nature. It selects and brings forward certain aspects of nature, while pushing other into the background. Ideas, attitudes, and practices that can be expressed in terms of secrecy-language are rendered prominent, while those that cannot are de-emphasized.302 Like the book metaphor, the metaphor of nature's secrets had been with mankind for a long time before the advent of modern science. Heraclit (ca. 550 - 480 B. C.) is supposed to have said that "nature loves to hide"; Cicero (106 - 43 B. C.) wrote that physics was concerned with "mysteries veiled in concealment by nature herself",3"3 and Plutarch (46 - 120) referred to science as the investigation of the "secrets of nature". However, according to Blumenberg (1960), antiquity was dominated in its attitude towards the truth - the truth about nature and its workings included - by the image of the "force of truth" by which the truth actively takes possession of man's mind. Citing Aristotle, Sextus Empiricus, and Thomas Aquinas he illustrates the widespread belief that the human mind is irresistibly affected by the power ("light") of the truth, and interprets it saying that Im umgekehrten Verhältnis zu der Macht, die der Wahrheit zugemessen wird, wird das Maß der eigenen Anstrengung um der Wahrheit willen stehen. Kein Zweifel, daß die Lebendigkeit der Metapher von der mächtigen Wahrheit einen gewissen Quietismus zum Korrelat hat.504 Contrary to this, the metaphor of secrets in its modern version is associated with the purposeful effort which must be directed against Nature's endeavour to preserve it. Galileo (1924, 1967: 68) believed that Nature did not make human brains first, and then construct things according to their capacity of understanding, but she first made things in her own fashion and then so constructed the human understanding that it, though at the price of great exertion, might ferret out a few of her secrets. The notion of a tiresome pursuit of the secrets of nature made the concept of science closer to that of a task, work, and collective activity. This aspect of the metaphor makes it an apt illustration of Lakoff and Johnson's (1980) claim that a metaphor is displayed in action at least as much as in language. In founding of the Royal Society of London lay the recognition that The work then being soe very great, It follows that it cannot be done by the endeavours [of a] single person not Indeed by the separate endeavours of thousands both these having been experimentally proved ever since the beginning of the world, but tis most probably done by the joynt unanimous and Regulated Labour of a multitude, this shews the necessity of a Society;505 its founders stated that Experimental Philosophy will prevent men's spending the strength of their thoughts about Disputes, by turning them to Works ... 3(12

Eamon 1994: 351-352. ibid.: 352. 304 Blumenberg 1960:23-24. 3115 Hooke, re-printed in Hunter and Wood 1986: 87. 3C * Sprat 1657, 1959: 334. 303

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Blumenberg (1960: 31) comments: So verwundert nicht mehr, daß bei Bacon zum ersten Male, im ersten seiner Essays, die Begriffe labour und truth im Zusammenhang eines Satzes auftreten. Hier endet eine über zwei Jahrtausende unangetastete splendid isolation der Wahrheit von allen Charakteren der Angestrengtheit ... [Der] im neuzeitlichen Wahrheitsbegriff angelegte 'Arbeitscharakter' der Erkenntnis ... wirkt sich pragmatisch ... in der Weise der Protektion und Zurüstung, des Methodenschliffes und der Institutionalisierung (Gründung von Gesellschaften, um die in Aussicht stehende Arbeit aufzufangen) aus ...

But before the metaphor of secrets of nature could become effective in the above-mentioned way, something had to change in the network of concepts of which it was a part. In the Renaissance and afterwards the notion of the "secret of nature" underwent two significant shifts. First, the concept of forbidden knowledge gave way to the notion of the deficiency of human knowledge. Second, the meaning of the phrase "secret of nature" as understood by natural philosophers became one with the meaning it had in the "books of secrets", popular handbooks of practical knowledge on how to produce certain effects; this associated the notion of nature's secrets with mechanical philosophy. Deficiency of human knowledge: the search for the new The first of the above-mentioned changes meant the elimination of the belief that the secrets were divinely and definitely hidden - that God purposely made certain natural things ultimately unknowable. It ended the humble resignation in the face of the unknown and encouraged competition against secrecy. The concept of "forbidden knowledge" stems originally from the Hermetic tradition of esoterism, where the "secrets of nature" ("arcana naturae") were accessible only to the chosen individuals, the ultimate source of their knowledge was revelation, and the initiated were obliged to keep them secret. Lactantius (260 - 317) thought that God made humans last in order to hide the mystery of the creation from them. The belief that the full knowledge of the natural universe was not intended for man accorded with the mistranslated and misunderstood biblical phrase "Noli alta sapere"307 widely circulated in the Middle Ages: the warning against spiritual pride in the original was translated into Latin and interpreted as a warning against intellectual curiosity. In the seventeenth century, though, the intellectual atmosphere of Europe changed so much that Bacon (Cogitata et Visa, 1964: 92) could argue that "it was a glory of God to hide a thing, and the Glory of a King to find it out; as if divine nature enjoyed the kindly innocence of such hide-and-seek, hiding only in order to be found, and with characteristic indulgence desired the human mind to join him in this sport". Natural things may be hidden, but they are not ultimately unknowable, and discovering secrets is not trespassing beyond the limits of permitted knowledge but a noble and dignified pursuit. From now on, the pursuit of natural knowledge becomes a competition against nature's endeavour to keep its important aspects unknown and mysterious. The metaphor becomes a frequent means to formulate the goals of scientific enterprise, as when Gilbert declares in "De Magneto" (1600, 1952: 11): 307

Cf. Ginzburg 1976. The warning was taken to refer to three kinds of "high" knowledge: arcana naturae, arcana Dei, and arcana imperil, in mutual reinforcement by analogy. The latter two kinds of secrecy served the interests of the Church and the state, respectively. All three were questioned at that period: by the new science, the Protestant movement, and Machiavelli's "Prince" revealing the secret mechanisms of politics.

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Very many subtile properties, as yet recondite and unknown, being involved in obscurities, are to be unfolded; and the causes of all these (nature's secrets being unlocked) are ... to be demonstrated.

The essential feature of this conception, from which the implication of the effort and ingenuity required of the scientist inevitably follows, is the fundamental distinction between how nature appears to be, and its reality, "between nature on the outside and nature on the inside, so to speak. According to this view, the sensible world is like a cloak or disguise within which 'real' nature hides".308 Galileo (Two New Sciences, 1974: 14) believed he was able to show ... how conclusions that are true may seem improbable at a first glance, and yet when only some small thing is pointed out, they cast off their concealing cloaks [le vestiche le occultavano] and thus, naked and simple, gladly show off their secrets,

and Bacon frequently wrote of "the need to penetrate into the inner and further recesses of nature", criticising the existing "speculation" for ceasing where light ceases ... Hence all the workings of the spirits enclosed in tangible bodies lie hid and unobserved ... unless these ... things ... be searched out and brought to light, nothing great can be achieved in nature.309

The support for this conception was provided, among other things, by the theory of Copernicus, the invention of the telescope which helped to correct certain misconceptions about the celestial bodies, and the invention of the microscope, all of which suggested the existence of a wide gap between appearance and reality. Thus, the metaphor of the secrets, defining the goal of science as the discovery of a deeper reality than the one which manifests itself to the naked senses in their common environment, powerfully contributed to the establishment of scientific method. From now on, in contrast to ancient science, the purpose of science is to find out new things, and not to demonstrate the necessity of the known as in antiquity and in the Scholastic philosophy. The latter kept science out of much of its subsequent territory, by restricting it to qualities and causes within the range of senses (taken to be identical with the range of intellect).310 Whereas classical science allowed neither singular nor contrived events a place in its scheme, the practices of numerous 17th century scientists, most notably those associated with the Royal Society of London, made them central aspects of their activities. First, attention was drawn to all which was "new, rare, and unusual in nature",3" which seemed to provide a key to the reality of 308 3M 310

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Eamon 1994: 352. Bacon: Novum Organum, 1620, I. 50. 1863, 8: 82-83. Scientia in medieval tradition was restricted to entities within the range of the senses; the invisible, so called "occult" qualities, perceived only by their effects, were conceived by medieval Aristotelians as unknowable or, alternatively, non-existent. After the invention of the telescope and the microscope, it had to be acknowledged that naked sense perception cannot be made the measure of things knowable. The Renaissance science accepted insensible qualities as causes of visible things; in fact, it recognised that all sensible qualities of bodies are products of insensible mechanisms, and that no properties of bodies directly enter the intellect. The notion of an "occult" quality or cause was retained in a changed sense (more or less, inexplicable by accepted principles of explanation, such as matter in motion), mainly as an object of criticism. Some, like Newton, did not concern themselves a lot with the "occult" character of e.g. gravity (force at a distance); occult virtues were acceptable if they could be reduced in number, generalized, not idiosyncratic to each kind of phenomenon. Cf. Hutchinson 1982. Bacon: Novum Organum, II. 29, 1863,8: 238.

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nature to a greater degree than the usual and well-known kinds of experience, the subject matter of classical natural philosophy. The search for new facts is one of the properties differentiating new science from old. Novelty is in high esteem: many titles of scientific books in the seventeenth century advertise their contents with the words "new" and "unheard-of". Secondly, contrived experiments began to be regarded as significant and legitimate means of acquiring knowledge about nature. The idea of a contrived experiment is a close associate of the idea of Nature trying to conceal her secrets: it is based on the belief that the course of events restricted to an A) artificial, B) local, historical setting (laboratory), could be representative of the ways of nature at large.312 This is expressed by Bacon (Advancement of Learning, 1605, 1970: 429) in the assertion that nature "exhibits itself more clearly ... under the trials and vexations of art", than when left to herself. Secrets, workshop, and mechanical philosophy The second of the changes in the notion of Nature's secrecy mentioned at the outset concerns the process which conceptually connected "secrets" with the mechanical philosophy. The above-quoted passages are symptoms of an approach to nature new to natural philosophers, but widespread in the so-called "books of secrets", which became immensely popular after the invention of printing. "Books of secrets" were related partly to magic, partly to mechanical arts. For Eamon (1994: 9), they were the "missing link" between medieval "secrets", embodying esoteric "forbidden knowledge", and Baconian experiments: they spelled the secrets out and made "magic" appear a matter of craftmanship. It is within "natural magic", constituting their subject matter, that we can find precedents for the later philosophical belief that the invisible realms of nature could be profitably entered by thought. In numerous books on natural magic written in that period, already in their titles the words "secret" and "experiment" appear side by side, expressing and stabilising the conceptual affinity between both. This facilitated the breakthrough of the idea that new knowledge could be acquired in an artificial setting rather than by observation in a natural one, the latter being how classical and scholastic science proceeded. "Books of secrets" played an important part in moving the "secrets of nature" from the sphere of esoteric, magic, occult, unknowable or knowable only by revelation or intuition, to the sphere of the mechanical, imitable, knowable, reducible to mechanical terms, explainable by interactions of physically existing parts. Such an explanation was the real goal of science; the Aristotelians merely named "occult causes" and "occult qualities", the new science wants Dear (1995: 158, 158 ff.), hedging his claim by saying that he only requires "the loosest and most permissive of the accepted senses of the word 'metaphor', asserts that 'to say that what happens in such a situation is what happens in nature is ... a metaphorical identification"; in an experiment, "artificial contrivances ... stand for other things not directly manipulable" (ibid.: 161). He illustrates his assertion with Guiffart's discussion of vacuum experiments using Torricellian liquid-filled glass tubes: '"In them one sees a little miniature of the world, in which, holding the enclosed elements in our hands, and at our disposition, they make known what they are and what they can do.'... The fact that one of Pascal's glass tubes puts constituents of nature 'at our disposition' is, of course, one of the primary characteristics of an experimental apparatus ... Guiffart portrays himself as applying to Pascal's glass tubes and their manipulation a characterisation that properly belonged to the world. Metaphors, as we have seen, tend to turn into practical identities when people start treating them that way, which is why Lakoff and Johnson have written of 'metaphors we live by'. Guiffart has started to live by a new metaphor whereby playing with glass tubes becomes identical to learning about the atmosphere" (ibid.: 159).

156 to analyse them in terms of matter in motion. The key to the methodology of new science was the notion of the hidden - "secret" - mechanical structure of nature, necessitating an endeavour to discover and describe it. The new age radically diminishes the classical distance between the scientific and the technical, the natural and the artificial, the knower's and the maker's knowledge, recognising a relation that exists between the increased knowledge of nature and Arts - techne. Bacon stated: The history of Arts ... takes off the mask and veil from natural objects, which are commonly concealed and obscured under the variety of shapes and external appearances.313 Charleton spoke of "Nature's Laboratory",314 Bacon of penetrating "all the secrets of Nature's workshop";315 for the latter, paper "imitates ... the skin or membrane of an animal, the leaf of a vegetable, and the like pieces of Nature's workmanship".316 The familiar metaphor of secrets of nature with its connotations borrowed from the books of secrets became an ally of mechanical philosophy: it helped dissolve the classical distinction between art and nature, since the expression "secret of nature" came to be understood as referring to a technique, reducible to mechanical terms, by which nature produces certain effects. Hooke hoped that showing natural objects in more detail, the newly invented microscope might bring about many admirable advantages, towards the increase of the Operative, and the Mechanick Knowledge, to which this Age seems so much inclined, because we may perhaps be inabled to discern all the secret workings of Nature, almost in the same manner as we do those manag"d by Wheels, and Engines, and Springs, that were devised by human Wit.317 The donor subject for personification of nature is here the human maker, a researcher, craftsman, or constructor. As the means used by human makers were of mechanical nature, personification facilitated and familiarised the idea that nature produced its effects by the same, that is, mechanical, means, as a man in his laboratory or workshop. The concept of occult qualities became replaced by the notion of mechanism which is unknown but in principle knowable and visualisable. The abolition by mechanical philosophy of the difference between art and nature, through the assumption that nature worked in the same manner as man-made artefacts, was of capital importance for the development of modern experimental science. Mechanical properties were projected from an artefact back upon nature whose effects they were meant to imitate. From the similarity of effects, the conclusion was drawn as to the similarity of the principles. At the same time, the hypothetico-deductive method became recognised as respectable and scientific in regard to the aims and objectives of science and began to be self-consciously adopted. Not only observation aided by mechanical instruments could provide knowledge of the hidden causes; even if not everything is knowable with certainty, it does not mean that the pursuit of explanation should be abandoned in the insensible realm. In view of this aspect of new methodology, the mechanism metaphor and the metaphor of the secrets of nature appear to be interrelated; we discuss this relation in section 5.2.2., dealing with metatheoretical function of the clock. 313 314 315 316 317

Bacon: Advancement of Learning, 1857-1874,4: 257. Charleton 1654, 1966: 342. Bacon: Novum Organum, 1863,8: 172. ibid. Hooke 1665, 1961. The Preface a: 10.

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Secrets and the gender of Nature For an 18th century scientist, Nature is not only an "alienated Other": it is an alienated She confronting a male cognitive subject. The traditional image of Nature as a woman contributed to the "secrets of Nature" the connotation of male curiosity about females, and of female modesty (cf. Schiebinger 1988). Nature intended to conceal her intimacy from those who would like to know her intimately. It had been an artistic topos to present Nature as a woman opposing the human endeavour to look under her robe, and the robe was frequently depicted as slightly damaged due to human attacks. The metaphor of secrets of Nature participates in the influential metaphorical complex of connotations concerning Nature and its relation to the scientist, guided in terms of gender. John Webster, emphasising the necessity of experimenting, worded his argument against the Aristotelians saying that they are wrong in thinking that "they can argue Dame Nature out of her secrets, and that they need no other key but Syllogisms to unlock her Cabinet". Merchant (1980) believes that it is the female gender of Nature which facilitates conceptually the notion that its "hidden parts" should be investigated "under the trials and vexations of art", as in this situation it "exhibits itself more clearly ... than left to herself",318 and interprets it as a hint at witches' trials accompanied by tortures by means of which one believed one acquired the truth.3" Bacon uses gender imagery to call for the establishment of "a chaste and lawful marriage between Mind and Nature", and elsewhere, he says again: "My dear, dear boy, what I plan for you is to unite you with things themselves in a chaste, holy and legal wedlock. And from this association you will secure an increase beyond all the hopes and prayers of ordinary marriages, to wit, a blessed race of Heroes or Supermen." ""Bacon's, and that means as well the period's, vision is that of a science leading to a soft sovereignty, tender dominion and mastery over nature, its command achieved by obeying its laws, "for you have but to follow as it were hound nature in her wanderings, and you will be able, when you like, to lead and drive her afterwards to the same place again".32' This spirit of desire to achieve mastery over nature, expressed in terms of gender, is an active spirit of doing, the conception of science as action, in accordance with the idea of active experimentation devoted to "finding out". In "The Masculine Birth of Time", Bacon applies sexual dialectics to praise the new science as "truly masculine"322 and to promise to his addressee ("boy") to "come in very truth leading to you Nature with all her children to bind her to your service and make her your slave" in contrast with the harshly-criticised ancient science, which was passive and speculative. 318 119

520 321 522

Bacon: Advancement of Learning, 1970: 429. Attributing a sexist attitude to Bacon, Merchant moves so far as to interprete the fragment "Neither ought a man to make scruple of entering and penetrating into these holes and corners, when the inquisition of truth is its sole object - as your Majesty [King James I, author of "Daemonology", a treaty on witchcraft] has shown in your own example" - as referring to the gynaecological examination during the trials of women suspected of having a sexual releationship with the devil. The thesis, however, is rather speculative. Bacon: The Masculine Birth of Time, 1964: 72. Bacon: Advancement of Learning, 1857-1874,4:296. The male-female distinction was frequently used to characterise the (male) literary style of the new science. Glanvill praises its "manly sense" opposing it to "fine metaphors and dancing periods", and attacks scholastic terminology maintaining that "these verbosities do emasculate the Understanding". Sprat anticipates the triumph of English in Europe as the language proper to expressing "the masculine arts of knowledge", in contrast to "our neighbouring languages" (meaning French) suitable rather for "the feminine arts of pleasure". Quoted in Vickers 1985: 44.

158 4.3.4.2. Terra incognita - science as a voyage; science as a conquest Today, the metaphor of "terra incognita" used within the scientific context is no more than a rhetorical device expressing the fact of missing knowledge, as when a science populariser says talking of a diagram on which the energy of particles is plotted against their mass: Nuclear scientists have progressed along the mass axis. This leaves the area distant from both the axes as a terra incognita waiting to be explored.323 Its role was very different in the period when the stunning geographical discoveries which began the Renaissance did not lie far behind: creating conceptual affinity between a territorial discovery and a scientific one actually encouraged the belief that what was done in geography can also be done in the knowledge of nature. Columbus' achievement had a considerable significance for the conception of knowledge acquisition: it documented that a substantial gain in knowledge about the world was to be had by means of action, instead of reasoning. "New World", the term originally referring to newly-discovered America, appears in the context of the improvements in the experimental equipment of science: By the means of Telescopes, there is nothing so far distant but may be represented to our view; and by the help of Microscopes, there is nothing so small, as to escape our inquiry; hence there is a new visible World discovered to the understanding.324 Sir Thomas Browne, in his "Pseudodoxia Epidemica", a compendium comprising corrections of popular misconceptions in all possible branches of natural philosophy, wrote: We hope it will not be unconsidered, that we find no open tract, or constant manuduction in this labyrinth, but are oftentimes fain to wander in the America and untravelled parts of truth. For though, not many years past, Dr. Primrose hath made a learned discourse of Vulgar Errors in Physics, yet have we discussed but two or three thereof.325 The cover page of Bacon's "Novum Organum", a treaty on natural philosophy, shows a ship setting off from the shore, and the voyage metaphor constantly reappears in his writings: In fact, had not political conditions and prospects put an end to these mental voyages, many another coast of error would have been visited by those mariners. For the island of truth is lapped by a mighty ocean in which many intellects will still be wrecked by the gales of illusion.326 That the metaphor not only decorates but also to some extent drives Bacons reflection on the scientific method is shown in "Cogitata et Visa" (1964: 92): In olden days, when man directed their course at sea by observation of the stars, they merely skirted the shores of old continent or ventured to traverse small land-locked seas. They had to await the discovery of a more reliable guide, the needle, before they crossed the ocean and opened up the regions of the New World. Similarly, men's discoveries in the arts and sciences up till now are such as could be made by intuition, experience, observation, thought; they concerned only things accessible to the senses. But, before men can voyage to remote and hidden regions of nature, they must first be provided with some better use and management of the human mind. Such a discovery would, without a doubt, be the noblest, the truly masculine birth of time. 323 324 325 326

ScAm 250, Jan 1984: 46. Hooke 1665, 1961. The Preface a: 10. Browne 1968,2: 178-179. 'To the Reader." Bacon: The Masculine Birth of Time, 1964: 69.

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For Blumenberg (1960: 61), the metaphor of terra incognita incorporates das spezifische Gefühl der ersten Jahrhunderte der Neuzeit für die Proportion zwischen dem Bekannten und dem Unbekannten, dem Alten und den noch anstehenden Neuen ... das eigentümlich Vor-theoretische, stimmungsmäßig Gespannte, Ahnungshafte einer Weltdeutung ... die sich am Anfang unermeßlichen Zuwachses an Erkenntnis wähnt und dies in Willentlichkeit, Arbeit, Methode, Energie umsetzt.

The comparison of the scientist to a sailor also introduced a strong implication of the conflict with established beliefs: the new scientist was prepared to learn new things, even those that opposed the claims of the ancients.327 The sense of desirability of working out new insights instead of repeating the old and worn-out Aristotelian dogmas was expressed in metaphorical terms by Glanvill (1661, 1970: 1): The Aristotelian philosophy is inept for New discoveries; and therefore of no accommodation to the use of life ... That there is an America of secrets, and unknown Peru of Nature, whose discovery would richly advance them, is more than conjecture. Now while we either sayl by the Land of gross and vulgar Doctrines, or ... by the Cynosure of meer abstract notions; we are not likely to reach the Treasures on the other side of Atlantick: The directing the World the way to which, is the noble end of true Philosophy. That the Aristotelian Physiology cannot boast itself the proper Author of any one Invention; is praegnant evidence of its infecundous deficiency ...

When Glanvill talks of the advantages from increasing natural knowledge in terms of "treasures" to be found on the other side of Atlantic, the "treasures" are of course used figuratively, but they do not stand for the sheer pleasure of intellectual enlightenment: they express the newlyemergent utilitarian attitude to science (before, the utilitarian was the domain of techne), of which Glanvill was an advocate. In view of the fact that the newly discovered territories were not only contemplated for the sake of cognitive gain, but also rather militantly appropriated, it is only logical that the metaphor drawing parallels between nature and the New World frequently takes a militant and possessive turn in which science appears as a conquest and appropriation of nature. Descartes (1960: 33) talks of the pursuit of scientific truth in terms of battles and victories: Car c'est veritablement donner des batailles, que de tacher a vaincre toutes les difficultes et les erreurs qui nous empechent de parvenir a la connaissance de la verite ...

The utilitarian theme of "stretching the deplorably narrow limits of man's dominion over nature"32' constantly reappears in Bacon, and Whitney (1990) argues that Bacon's "New Atlantis" constitutes a proposal of the scientific methodology which uncovers his colonial predilections. But the most specific reference to the donor subject of this conceptualisation of science is to be found in Hooke (1986: 87): ... though mankind have been thinking these 6000 years and should be soe six hundred more yet they are and would be much whereabouts they were first, wholly unfit and unable to conquer the difficulty of natural knowled [ge]. But this newfound land must be compelled by a Cortesian army well Disciplined and regulated though their number be but small.

527 528

E.g., Aristotle claimed that the antipodes cannot be inhabited. Bacon: The Masculine Birth of Time, 1964: 62.

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4.3.4.3. Science as venatio When a contemporary scientist talks of "the search procedure used to hunt for narrow e+eresonances",329 he is unconsciously evoking a very popular member of the pack of intertwining metaphors which early modern science used in order to conceptualise and verbalise the pursuit of natural knowledge: the concept of the hunt, science as venatio. The hunt unites in one concept some elements of the three aforementioned metaphors shaping the relation between science and nature: secrecy, journey to an unknown place, and conquest. It is conceptually congruent with the metaphor of secrets and reinforces it: "hunting" as applied to science means a pursuit, "finding out" nature's hiding place in a forest. Hooke (1665, 1961, The Preface a: 9) believed that ... the footsteps of Nature are to be betrac'd, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in endeavouring to avaid our discovery.

The notion of science as a hunt expresses and stabilises the idea of a conjectural scientific methodology based on recognition from traces, noticing apparently insignificant facts, proceeding to concealed things from inconsidered or unnoticed details, a methodology based on experience, practical skills and practical intelligence, which, for the ancient Greek, led not to scientific knowledge but to the kind of knowledge they called metis and differentiated from science.330 Bacon coined the expression "the Hunt of Pan" to refer to the experimental pursuit of natural knowledge (Learned Experience ... which is ... a kind of hunting by scent),331 and Gassendi compared the acquisition of knowledge about the hidden aspects of nature to a hunting dog finding a footprint or a scent and sniffing his way to the prey (cf. Eamon 1994: 283). A Venetian society for the pursuit of natural secrets founded in 1596 called itself "Accademia Cacciatore" - Academy of Hunters, another, founded in Bologna in 1665, "Accademia della Tracia" - Academy of Traces. The classical vision of the essence of reality open to the senses and knowable by reason, emitting "the light of the truth", gives way to the vision of bounty, variety, a dense forest, a labyrinth,332 preventing the human being from having immediate insight. Significantly, if the knowledge of hidden principles may be acquired by considering novel, unexplained facts, that means that collecting such facts, not yet embodied in any theory, becomes a part of an inquiry into nature - like in the tradition of natural magic, but contrary to ancient science, indifferent to any "curiosities". The activities of the Royal Society of London included the collecting of singularities - rare, unexplained data as visible clues - which, if followed and read properly, might lead to later discoveries: No Observation or Experiment ... is therefore to be slighted, because it may seeme to be but mean. For so far as we have any matter of fact before us, we have really advanced further than we were before. And many things that seem trivial in them selves, may be a foundation for that which is of greater moment.5" 329

Physical Review Letters 33, 1974, No. 24: 1453. "° For Aristotle and medieval science, science was the state of capacity to logically demonstrate the universal and necessary causes of known facts, to show how they follow from first principles. "' Bacon 1857-1874,4: 411,421. "2 The metaphor of labirynth appears e.g. in Bacon's "Novum Organum" I. 98. "' Royal Society Miscellanous MSS 4.72, re-printed in Hunter and Wood 1986: 66.

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The conceptual transfer from hunt as the donor domain to science as the recipient domain focuses on the "finding out" aspect of the hunt and excludes one of the essential features of the donor domain - the destruction of the object of hunting. Noticing this variance in the donor and the recipient subjects, Bacon does away with it, stressing the difference between the experiment in which the prey is killed and the experiment in which it is caught, which he regards as the proper aim of science. The image of hunting through the forest for a hidden location is isomorphic with Bacon's (1964: 69) voyage to "the island of truth ... lapped by a mighty ocean in which many intellects will still be wrecked by the gales of illusion". There is also an obvious affinity with the concept of a conquest, a victory in a competition culminating in the appropriation of the object of the hunt, as well as with the concepts of a sexual relationship and marriage in their connotations of domination and appropriation. All the metaphors outlined above contain elements by which they collectively point in one direction: that of a science which is active in its approach to nature, using experiment as the means to gain knowledge, allied with technical disciplines, and oriented towards utilitarian goals - the mastery and manipulation of nature. All these features of the approach of contemporary science to its subject matter emerged during the Scientific Revolution and have survived without any significant changes until now. We argued that their formation was dependent to a large degree on the possibilities of conceptualisation offered by the structure of other domains of reflection, which brought in their own associations and reordered the existing ones. The metaphors served as "structure organisers" and provided the whole scientific enterprise with a guidance, the role of which we can probably never fully apprehend, being confined to viewing them from a conceptual perspective which they have themselves helped create.

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5. World theories in meta-theory and the concept formation 5.1. The notions "world theory" and "world model" "World theory" is an extended metaphor whose recipient domain is not confined to a particular class of physical phenomena but embraces the whole of natural phenomena. Thus, any world theory presupposes the principal unity of nature. It constitutes a programme for the explanation of nature providing a set of theoretical concepts to be applied as basic explanatory categories, or methodological postulates, or both. This description of the function of world theory suggests affinities with "absolute metaphor", which we have situated on the meta-theoretical level of scientific discourse. Of all the metaphors of physics, world theories are the most multi-faceted and complex: their contribution to physics is situated both on the level of theory-making and formation of scientific concepts, and on the level of pre-scientific assumptions and methodological postulates constituting the general approach to the question of what constitutes natural science. Because of the universality of a world theory, its theoretical assumptions are assumptions about the nature of physical reality, and a differentiation of its tissue into the two aspects cannot be done neatly. The most widely acknowledged metaphorical world theories in the history of science have been anthropomorphism and mechanism as sometimes competing, sometimes interactively related conceptualisations of the physical universe. Whereas anthropomorphism played a greater role in the earlier stages of the history of ideas, mechanism has taken the upper hand in modern times. The third grand "world theory" pertaining to the development of natural science is the metaphor of the world as a text, which we also include in our survey. World theories are not restricted in their application to the field of science and philosophy, but also pertain to common thought and language, which links them to "underlying metaphors". Particularly anthropomorphisms in physical science may be regarded as scientific implementations of a commonplace kind of transfer. A difference between the mechanism and text metaphor on the one hand, anthropomorphism on the other is that while the former are products of a (relatively late) invention, the latter has been with mankind since pre-historic times, invisibly (unreflectingly) present in language and conceptual representations of numerous domains. Hence, we have chosen to place anthropomorphism among the "underlying metaphors" in the preceding chapter (we could have done otherwise). Dealing with the mechanism metaphor, some authors use the term "model", speaking of the clock, or more generally a mechanism, as a model of the world. We have also used the notion of model to refer to the theoretical aspect of the clock metaphor. We think that this term is apt in so far as the clock metaphor establishes a set of basic theoretical concepts (material elements having size and shape, motion, transfer of motion through push and pull) to be applied in the analysis of processes of nature, and produces concrete explanations of particular physical processes. Also anthropomorphism providing explanations of physical processes in terms of basic principles imported from human psychology (sympathy, antipathy) may be regarded as a simple world model. A world model, then, is a particularisation of a world theory, which is more abstract and may generalise over several alternative world models.

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5.2. World machine 5.2.1. The clock metaphor The comparison of the world to a machine can already be found in Lucretius (ca. 99 - 5 B. C.), who talks of "machina mundi", but the connotations of this notion in antiquity were quite different from those in the late Middle Ages and afterwards. According to Blumenberg (1960), the donor subject for "machina mundi" was the automata used on the stage during theatre performances ("deux ex machina"), and the metaphor highlighted and projected upon the world quite different features of the machine33'1 than the mechanist clock metaphor or later the machine metaphor of the industrial revolution. The attractiveness and even self-evidence of the clock as a model for the world, or a donor subject of the metaphor, was entrenched in its function: the clock simulates the daily movement of the celestial spheres. The first clocks were built mainly not for telling the time, but for simulating the astronomical motions. Only later does the clock undergo the debasement from an astronomical masterpiece to a mere time-teller. At the same time as clocks simulating astronomical movements, automata simulating animals and rational behaviour were built throughout the late Middle Ages and during the Renaissance. This desire for simulacra was a factor which led to the growth of mechanical skills, which in turn found its reflection in mechanical philosophy (cf. De Solla Price 1964), whose central assumption was that each act of rational behaviour as well as the cosmic phenomena were reducible to the workings of a mechanical device. The perfection of technology which made possible the construction of still more perfect automata resulted in the idea that nature could be simulated by a rich and complex mechanism and, in effect, that its functioning depended on the same principles which moved the man-made devices. The mechanistic metaphor informed the attempts to describe physical phenomena in terms of aggregates of moving elements such as Boyle's or Digby's mechanical explanations of electricity, Descartes' explanation of gravity, Newton's explanation of colours through rotation of particles with different angular speed, etc. The comparison of the universe with the clock-like mechanism was an incorporation of a basic methodological postulate of early modern science: the principle which Laudan called the principle of the multi-level identity of nature. The same principles were supposed to govern the whole macroscopic universe as those which we see in operation in man-made devices of man-scale dimensions; accordingly, the laws of nature applicable to visible massive bodies were also taken to apply to objects which are too small to be measured or observed. This principle, invalidated in the present day by the developments in particle and quantum physics, was formulated by Boyle (1772,4: 72) in the following way: To say, that though in natural bodies, whose bulk is manifest and their structure visible, the mechanical principles may be usefully admitted, are not to be extended to such portions of matter whose parts and texture are invisible; may perhaps look to some, as if a man should allow, that the laws of mechanism may take place in a town clock, but not in a pocket watch.

In the natural world of matter the reasons of motions are the same on all levels as in artificially constructed machines. Christian Wolff (Cosmologia Generalis, 1964,2,4: 104) asserted that "Mundus propemodum se habet ut horologium automaton"; he confirmed the Briefly subsumable as the dramatic and spectacular aspect of the universe.

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principle of the conservation of force (momentum) and explained it by pointing to the convertibility of a perfect watch and the world (cf. Wolff 1720, 1740). Leibniz (1978,7: 265) referred to the world machine, claiming that in nature everything must be explained "per magnitudam, figuram and motum, id est per Machinam". For him, the metaphor of the world as a machine includes the components perfection, automation or self-sufficiency (no intervention from outside), and regularity or determination. He criticised Newton's idea that the amount of motion present in the world decreases with time and God has to supply some additional motion to it, summarising it in the anecdotal "God needs to rewind his clock from time to time".™ In Descartes, the comparison between nature and machine was lifted to the central position in his explanation of the material world: I have hitherto described this earth, and generally the whole visible world, as if it were merely a machine in which there was nothing at all to consider except the shapes and motions of its parts."* Here, we see Black's "interaction view" illustrated: not only the notion of the world but also the donor subject, the machine, is modified in the act of comparison; some aspects of it are focused upon, others marginalised; the notion of the machine is reduced to parts, shapes, and motions. Other features such as human agency or wearing out or going out of order are suppressed. The notion of the machine became stripped of other characteristics which we can recall on reflection: our perception of it has been shaped by the mechanist world view. Briefly, the properties of the clock as the donor subject for the world highlighted in the juxtaposition and projected to, or emphasised in the conceptualisation of, the recipient subject were: • pre-determination, ultimate predictability in terms of chains of causes and effects, • no need of external intervention, automatic course of processes, • perfection, • repetitiveness, • the origin in the intentional act of the watch-maker,337 • mathematical encompassibility,338 • motion is the essential phenomenon to be accounted for, • all processes are translations of motion between parts (matter in push and pull), • the functioning of the whole is explicable in terms of the functioning of the parts, • it is possible to have all the component parts simultaneously in view.339 Contemporary physics has regained some of the features this view relegated out of existence, such as the individuality of each event, indeterminacy, and the fact that the scale of a process is not indifferent to its principles. 355 336 337

338

339

Leibniz 1934: 192. Descartes, quoted inTurbayne 1970: 67. God was frequently referred to as watch-maker in the 17th and the 18th centuries. An appeal to God as the ultimate causal factor in the physical universe (as "the first mover", and the primary source of regularities in nature) was still unproblematic in the time of the scientific revolution, cf, for example, Newton's "Principles". Some authors argue that it played the major role in the appeal of this metaphor in the eighteenth century, as the physical science became growingly mathematical; it made possible a union of mathematical and mechanical directions in the physical thought which were dissociated or even contradictory at earlier stages. This is necessary for Laplace's demon to function.

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The clock metaphor is as much an effect of the world being perceived in these terms as it is a causal factor in such perception. The metaphor is a summarising expression of the mechanical features detected in the world, subsuming them in a single and visualisable concept. After it has been called into existence, however, it performs the usual function of the conceptual metaphor which is to confirm, stabilise, and refine the conception of the recipient subject in which it originated. The above list is a selection of the properties of the clock which were taken over into the mechanistic world model as properties of the world. Other focusing is conceivable, which could connect the same couple donor-recipient subject along different lines, providing different conceptions of the world or calling forth different methodological trends in physical science. (Other conceivable similarities between the clock and the world apart from those listed above could be, for example: the clock is similar to the world because we can easily disturb its functioning; because it can show time incorrectly; because we can set it anew at our will; because the mechanical clock can be replaced by other time indicators such as a sand or water clock or a sundial, etc. Each of these properties of the clock has some cognitive potential if applied to the world as the recipient of the metaphorical juxtaposition, and its projection upon it could have inspired some new directions in thinking had it ever been highlighted by an appropriate conceptual context and seriously contemplated.) In every metaphor in which the donor subject is of sufficient complexity, only some of its aspects become highlighted by a metaphor. In the case of the clock metaphor, too, the focusing upon some features of the donor subject and their transfer to the recipient subject proceeded along the lines determined by the existing frame of thought and the potential for conceptual extension which this frame included. An aspect of the mechanist metaphor is its relatedness to organism. Comenius (1970: 103) wondered at the invention of the clock which to him seemed similar to an animate object, showing that initially the metaphor of the world as machine did not necessarily appear as countering the earlier animist metaphor of the world as a living being:34" Is it not a truly marvellous thing that a machine, a soulless thing, can move in such a life-like, continuous, and regular manner? Before clocks were invented would not the existence of such things have seemed as impossible as that trees could walk or stones speak?

Here, the regularity and continuity of the machine makes it look like an imitation of a living being, which was motivated by the success of mechanical engineering in actually constructing such imitations, mainly as parts of clockworks of the cathedral clocks, such as those of Strasbourg Cathedral (built in the 14th and 16th centuries). Later on, the direction of comparison was reversed. The idea that the mechanical art is a glorious imitation of Divine Creation341 led eventually to the mechanism becoming the donor subject for conceptualisations of living beings in mechanical terms. E.g. for Maupertuis (1756, 1974,1: 14),

M

" The cultural relativity of the mechanism and the organism being mutually exclusive categories has been anecdotally illustrated by Boyle, who reports in "Hydrostatic Discourses" of a Chinese emperor having received a watch from Jesuit missionaries. In spite of having explained its functioning to the monarch in every possible detail, Boyle failed to convince him that it was not endowed with life. Cf. Dear 1995: 153. 541 Cf. Haber 1975. He quotes a sixteenth century poet Philip Nicodemus Frischlin, whose well-known poem glorified the building of second clock of the Strasbourg Cathedral by Dysypodius as a display of genius similar to God's.

166 "Les corps des animaux et des plantes sont des machines trop compliquees". MacCormac (1985: 36) remarks in this context: Perhaps a new figure of speech should be invented, 'mechanification', the transformation of the living into the mechanical, a process that has been with us since at least the seventeenth century. Turbayne (1970: 213) believes that the popularity of machine metaphor results form the fact that we are familiar with force and power in ourselves, and most of us use machines at various times. We are in general more interested in machines than in language, and are fascinated by them. We are fascinated because they resemble us. It is as if they can make and do things without any help. It is as if they contain forces or powers which produce their movements. This factor partly accounts for the early success of the machine metaphor and its continued success. In this view, the machine owes its attractiveness as a donor subject to its apparent similarity to the most familiar objects of our perceptions, that is, ourselves. This idea is akin to what de Sola Price says about the early fascination with the machine as being rooted in its ability to simulate human behaviour. This demonstrates the "interactivity" of the donor and recipient subjects of the metaphor: the machines provide concepts to explain the world with, but they are chosen as a donor domain because they seem similar to man, who used to be the main explanatory principle for the world in earlier stages of the history of ideas. In this sense, we come to the somewhat surprising conclusion that the theory of the world as machine may be regarded as a conceptual development out of anthropomorphic world theory. The set of concepts provided by the machine as the donor domain is different from the set of volitional, hylopsychic notions won out of man in this earlier stage; and this new set of concepts becomes, in turn, applied to man as the recipient subject. It is, however, not altogether free from anthropomorphism - since Newton, the mechanical universe has contained "force", conceived with the help of a metaphorical projection out of the human sensomotoric experience. Eventually, the organism and the mechanism came to be conceived as two alternative and competing sorts of explanations. Kepler's astronomical thought was already guided by the opposition of the pre-scientific animist world model and the clock metaphor: Meine Absicht ist zu zeigen, daß die himmlische Maschine nicht wie ein göttliches Lebewesen ist, sondern wie eine Uhr.342 The analogical perception of the machine and the organism reappears, in a different theoretical garment, in the nineteenth century, which we shall deal with in the next section (5.1.2.). The way in which the metaphor of the clock-like nature of the world contributed to the formation of the mechanist theory of nature, which explained all physical phenomena as the effects of the pull and push of moving matter, is the most evident and generally acknowledged aspect of the clock metaphor. As pointed out by Laudan (1966), it also had another facet, pertaining to the methodological aspect of science. Focusing upon a different aspect of the clock than those which supported the mechanist theory of nature, it helped to vindicate probabilism as a methodological principle. The comparison of the universe with the clock stood in close relationship to Descartes' "hypothetical" view of scientific research, that is, to resignation in the face of the recogniti"Scopus meus hie est, ut coelestem machinam dicam non esse instar divini animalis, sed instar horologii." Kepler 1859, 1977,2: 84.

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on that a scientist must be content with hypothetical principles and conjectures rather than true and valid inductions. The clock to which Descartes compared the universe was one whose internal mechanism was not seen. Its internal parts could only be conjectured about on the basis of exhibited behaviour. Descartes (1897-1957,9: 322) recognised that nature was describable (or explicable) in a variety of ways and the fact that an explanation worked was no proof that it was true: Just as an industrious watch-maker may make two watches which keep time equally well and without any difference in their external appearance, yet without any similarity in the composition of their wheels, so it is certain that God works in an affinity of diverse ways (each of which enables him to make everything appear in the world as it does) without making it possible for the human mind to know which of all these ways He has decided to use.

The watch whose interior is forever excluded from our view may be constructed in any number of ways, and a physicist honours his commitments sufficiently if he conjectures some possible mechanism compatible with the phenomena at hand. As "a mechanic with experience of machinery ... can readily form a conjecture about the way its unseen parts are fashioned", so the mechanist philosopher seeks "to investigate the insensible causes and particles underlying ..."M3 Laudan (1966: 78) argues that The clock analogy is not merely an afterthought which Descartes threw in to illustrate his argument. Rather, it formed an integral part of his way of looking at the world and the role he assigned to the corpuscular philosophy in explaining the world.

Like Descartes, Boyle (1772,2: 45) uses the clock metaphor to justify the necessarily hypothetical character of scientific theorising:3*1 For as an artificer can set all the wheels of a clock a going, as well with springs as with weights ... so the same effects may be produced by divers causes different from one another; and it will oftentimes be very difficult, if not impossible to say ... which of those several ways ... [nature] has really made use of to exhibit them.

This facet of the clock metaphor becomes commonplace among the eighteenth century writers, reappearing, for instance, in d'Alembert (1767,4: 258-59): Nature ... is a vast machine whose inner springs are hidden from us; we see this machine only through a veil which hides the workings of its more delicate parts from our view ... Doomed as we are to be ignorant of the essence and inner contexture of bodies, the only resource remaining for our sagacity is to try at least to grasp the analogy of phenomena, and to reduce them all to a small number of primitive and fundamental facts.

The developments in physics outdated the clock metaphor as an expression of the mechanist philosophy, but its aspect relating it to hypothetical view of scientific research, dating back to Descartes, has survived as an exegetical metaphor till the present day. Einstein and Infeld wrote as late as in 1956 in a popular scientific exposition of the historical development of physical science: Physikalische Begriffe sind freie Schöpfungen des Geistes und ergeben sich nicht etwa, wie man sehr leicht zu glauben geneigt ist, zwangsläufig aus den Verhältnissen in der Außenwelt. Bei unseren Bemühungen, die Wirklichkeit zu begreifen, machen wir es manchmal wie ein Mann, der verDescartes: Principles of natural philosophy. Quoted in Turbayne 1970: 212. Cf. also Royal Society: Boyle Papers, 2: 141.

168 sucht, hinter den Mechanismus einer geschlossenen Taschenuhr zu kommen. Er sieht das Zifferblatt, sieht, wie sich die Zeiger bewegen, und hört sogar das Ticken, doch hat er keine Möglichkeit, das Gehäuse aufzumachen. Wenn er scharfsinnig ist, denkt er sich vielleicht irgendeinen Mechanismus aus, dem er alles das zuschreiben kann, was er sieht, doch ist er sich wohl niemals sicher, daß seine Idee die einzige ist, mit der sich seine Beobachtungen erklären lassen. Er ist niemals in der Lage, seine Ideen an Hand des wirklichen Mechanismus nachzuprüfen.345 And in 1988, Bruce Gregory wrote in a popular scientific book on modern physics: Someone once likened studying the nature of matter by using a particle accelerator to studying the mechanism of a watch by smashing it against the wall and looking to see what pieces fly out.346 This illustrates the process mentioned by Boyd (1985) in which a metaphor which used to be instrumental and stimulated scientific research at one stage becomes merely exegetical and decorative at a later one. 5.2.2. The world as a working machine The attractiveness of the clock as the explanatory model for the world evaporated about the end of the eighteenth century. Whereas the clock was the prototypical machine in the Middle Ages and the Renaissance, this situation changed rapidly in the late eighteenth century: at that time, machines were developed which supported men in the working process. The mimetic function of the machine in its prototypical realisations as the clock and the figurine in the Middle Ages and the Renaissance, which made it an appropriate model for the world as well as for an organism, was gradually suppressed from the position of the central aspects of the mechanical. When the machine as metaphor for the world reappeared in the nineteenth century, by this time the industrial revolution had significantly changed its image (its stereotype, prototype, semantic structure, or semantic field, whichever kind of description one prefers). The prototypical properties of the machines of the late eighteenth and the nineteenth century were: - the function of performing productive activities which had previously been performed by men; - with the invention of the steam engine, the mechanism transferring motions between parts was accompanied by an engine transforming a substance into useful work. As far as causal thinking is concerned, the metaphor of the world as a working machine may be viewed as a conceptual continuation of the clock metaphor of early modern science; Breger (1982: 157) speaks in this context of "Beziehung zwischen einer an Maschinen geschulten Deutung der Natur und dem Bestreben, Naturvorgänge kausal zu erklären". Notwithstanding this continuity, the change in the donor subject led to considerable changes in the set of features of the world highlighted by the metaphor: while the fascination with the clock was disconnected from its utilitarian function, in the nineteenth century the machine is primarily fascinating because of its utility in the industrial environment. The interest in nature becomes associated with the perspectives for its useful application in working processes:

345 346

Einstein and Infeld 1956: 22. Gregory 1988: 145.

169 Wenn die Mechanisten des 17. und 18. Jahrhunderts sich auf die Uhr als Modell der Naturbetrachtung beriefen, so dachten sie nicht an von der Uhr ausgehenden Kraftwirkungen, sondern an ihren aus verstehbaren Ursachen erklärbaren gleichmäßigen Lauf; dieser war das Modell für die Gesetzmäßigkeit der Bewegungen im Kosmos. Die das 19. Jahrhundert faszinierende Maschine symbolisiert nicht die gleichmäßige Bewegung, sondern das Verrichten von Arbeit."7

With the development of the engine and, with it, of thermodynamics, the transformations of energy become the most important aspect and principle of explanation for the physical world. Thermodynamics provided a new pattern of similarities between the machine and the world, which could not be conceived of in the old theoretical scheme. For example, just as no machine has one hundred percent efficiency, so there is dissipation of energy in the world as a whole.348 The association of human effort and the mechanical activity of machines on the one hand and the metaphor of the world as a working machine on the other, led to the establishment of the concept of (mechanical) work with its anthropomorphic naming, to the development of the concept of energy and the establishment of the principle of its conservation. The concept of energy can be traced back to its roots in two domains, interactively influencing the conceptualisations of each other. On the one hand, the invention of the steam engine converting heat into mechanical work led to the idea that there is something common to each of them, of which they are both manifestations. The other source of the concept of energy is physiology - the observation that the animal or human organism is capable of both producing heat and performing mechanical work. It was however only by comparison with a machine that this property of organisms could be noticed and identified as a significant fact of physiology and physics. After a certain decline of the popularity of iatrophysics in the eighteenth century, the change in the image of the machine made possible the revival of mechanism in physiology about the 1840's (cf. Breger 1982: 155). The essential feature of the machine as the donor subject of the mechanist metaphor, which led as a consequence to the development of the concept of energy and the principle of its conservation, was the work which it performed at the cost of what had to be supplied to it in order to make it function. Nature came to be conceived of in the same terms: its forces and their effects were to be measured in the same way as those of machines, that is, in units of mechanical work. The processes taking place in nature came to be interpreted from this perspective. All changes are brought about by forces of nature reducible to quantities of mechanical work and their quantitative treatment should be in units of mechanical work, advanced this way to the position of a primary, most central, prototypical, salient kind of a physical process. Helmholtz (1896,1: 227) formulated this conception saying: Alle Veränderung in der Natur besteht darin, daß die Arbeitskraft ihre Form und ihren Ort wechselt, ohne daß ihre Quantität verändert wird. Das Weltall besitzt ein für alle Mal einen Schatz von Arbeitskraft, der durch keinen Wechsel der Erscheinungen verändert, vermehrt oder vermindert werden kann. The authorship of the principle of the conservation of energy is attributed, among others, to J. R. Mayer, a German medical doctor who in 1842 published his ideas about the equivalence Breger 1982: 157. Interestingly, the recognition of the dissipation of energy has been reformulated for educational and expressive purposes by means of an animist linguistic metaphor as the universe moving towards the "cosmic death", see page 211. This is another example of turning to the organic for support and inspiration in expressing the insights of physics.

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of heat and mechanical work. In his publications the relation between the mechanist approach to nature including physiology and the principle of quantitative equivalence of different forms of work is clearly displayed. Mayer proclaims the conservation of "force" for all kinds of "forces", uses mechanical work as the measure of "force" and calculates the mechanical equivalent of heat. He criticises contemporary physics for neglecting the relationship between heat and mechanical work - the entities created and disappearing at each other's cost in a physical process. Causes and effects are to be measured in the same units independent of the form they appear in, that is, in units of mechanical work; this amounts to the concept of the mechanical equivalent of heat. The formulation of the principle of the conservation of energy by Mayer as a result of his observations made in the domain of human physiology was only possible owing to the mechanist metaphor dominating German physiology at this period. The purpose of his analysis of the process of combustion in "anorganischen Bewegungsapparaten", steam engines, is to apply the recognitions gained in this way to processes taking place in organic beings. He draws numerous parallels between the steam engine and the animal organism. The ability of an organism to transform chemical energy into mechanical is analogous to the ability of gases to transform heat into mechanical work, permanent gases being analogons of cold-blooded animals and vapours being analogons of warm-blooded animals. In all these reflections the steam engine plays the role of the central object of comparison. Mayer holds the ability to perform mechanical work to be the most important product of animal life and wants to make it the basis of a new approach to physiology in spite of the inevitably absurd consequences of this view - such as the statement that "Die Leistung eines Mannes, der mit großer Anstrengung ein Gewicht frei hält, oder stundenlang unbeweglich gerade steht usw. ist = Null".349 Instead of recognising that this fact makes mechanical work unsuitable as a point of entry for the analysis of physiological processes, Mayer accepts it as a bare fact of physiology. He goes so far as to argue that hunger depends on mechanical work performed and not on the effort "put into" a process, and to measure the severity of an illness with the decrease in efficiency conceived as the ratio of consumed food to the ability to perform mechanical work. The activities of animal organisms are reducible to mechanical work, just as all qualitatively different types of natural agents, such as chemical, electric, magnetic, or thermal, can be reduced to their ability to lift a weight. On the way towards the formulation of the principle of the conservation of energy, the mechanist metaphor goes hand in hand with an ontological metaphor: a substantial conception of energy. The approach to what later receives the name of energy is based on an underlying analogy with indestructible matter: all changes in nature are changes of form of one constant or another. Thomson and Tait (1867,1: VI) say that "Energy is as real and indestructible as Matter". Mayer's conceptual point of entry is an analogy between "force" and matter: "Indem Mayer Materie und Kraft analogisiert, sieht er die Kraft als etwas an, von dessen Verbleib Rechenschaft abgelegt werden muß - ebenso wie der Chemiker mit Hilfe einer Waage vom Verbleib miteinander reagierender Stoffe Rechenschaft ablegt".350 The mechanical force is conceived here as a substance playing the role of a causal agent in all natural processes. This substantial conception of energy, manifesting itself by insisting on the equivalence of causes and effects, amounts to suppressing the directionality of the irreversible physical processes (such in which a may cause b, but not vice versa). For Mayer, "Kräfte sind "' Mayer 1842, 1978: 151. 350 Breger 1982: 174.

171 Ursachen"; as such, they are indestructible and equivalent to their effects. The substantial conception of energy also underlies Mayer's rejection of gravity being a force; only what is consumed in the act of causing an effect is a cause, and he sees gravity as a property of matter rather than a force (synonymous for him with a cause) as it does not obey the principles of calculation of the balance between causes and effects. It also prevents him from concluding that heat must be a form of motion, drawn later by Joule and Helmholtz from its ability to cause motion. It is frequently the fate of theoretical concepts bom in metaphorical processes to survive the deaths of theories to which they owe their birth. Although by the end of the nineteenth century the view of nature based on the mechanism metaphor had become outdated, indestructible energy, dissociated from the mechanical approach which used to form its conceptual roots, survived until the present day as the basic concept of modern physical science. 5.2.3. Man and machine in information theory At the present day, the machine as an analogen of an animal and human being reappeared in the form of an electronic device, the computer. The properties highlighted by this analogy are, however, quite different than the mechanical properties which formed the focus of interest of mechanical philosophy. For Norbert Wiener, the founding father of cybernetics, the main part of the analogy lies in the fact that The synapse in the living organism corresponds to the switching device in the machine ... The machine, like the living organism, is ... a device which locally and temporarily seems to resist the general tendency for the increase of entropy. By its ability to make decisions it can produce around it a local zone of organisation in a world whose general tendency is to run down."' The analogy between computers and organisms places them within the same, newly emergent category: entities diminishing local entropy, providing for the development of the notion of information and notions pertaining to its processing (memory, communication, etc.). Thus, it forms the corner stone of the ideas of cybernetics and information theory. Today, the mode of description of physical processes involving the notion of communication between physical systems is gaining currency e.g. in chaos theory. Halliday and Martin (1993) point out that the concept of communication, which has ripened on the basis of the category amalgamating men and electronic machines as entities capable of signalling and processing signals, is on its way becoming the "root metaphor" of contemporary science, the donor subject in a world theory.

5.3. The world as a text In this section we want to touch upon the impact of the book and writing as a metaphor for the world on the development of modern physical science. The level at which this contribution is situated is to be identified as meta-theoretical; the metaphor does not provide any particular theoretical notions nor hypothesis, but it shapes the intellectual context of doing science, as well as perceptions of its possibilities, significance, dignity, perspectives, and desirable methodology. 351

Wiener 1954: 31.

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The book metaphor was also frequently applied before the beginnings of the scientific revolution in the 17th century. Changes in the configuration of the intellectual context which took place at the latter period allowed the metaphorical pairing of writing and the world to come to be associated with issues relevant for the development of science, and to function as a guide of thought with respect to these issues. In what follows, we will show how the concept of a book which was the donor subject in the projection received a different focus (i.e. different elements of it were highlighted by the juxtaposition and metaphorically projected upon the world as the recipient subject) than when the same pair of the donor and the recipient subject was used before the scientific revolution, and analyse the particular conceptions for which the book metaphor functioned as a guide or structure-organiser. Before the scientific revolution, the metaphor of the world as a book written by God to be read by human beings had already been with mankind for centuries. In his broad collection of quotations of literary metaphors in which the book or, more generally, writing functioned as the donor subject, Curtius (1954) includes e.g. Plotinus' (205 - 269/270) description of the stars as letters composing a text which can be read by a reader knowing the alphabet the fortune-teller, the augur. The aspect of the metaphor which appears here is typical of the period prior to the scientific revolution. Associated with the semiotic, astrological applications of astronomy, it focuses upon the signifying aspect of visible language: upon the notion of an encoded message referring to a domain of reality different from the material in which it is written, of one thing being designated by another. This sense of the book metaphor as applied to the world of natural phenomena survived till the late Renaissance within a conceptual context very different from that of modern science. Late medieval and Renaissance science constituted an elaborate system of analogies and correspondences, where constellations of objects and processes constituting one domain (e.g. astronomy or plant anatomy) could be read as pointing to, that is, containing information, on another domain (e.g. politics or medical treatment). Accordingly, in the Middle Ages as well as in the Renaissance, the world was a book in the sense of containing a decipherable message, consisting of objects functioning also as signs - pointing outside themselves in possessing reference, as part of analogies or correspondences intended to be discovered and utilised.352 The transition to modern science was accompanied by a change of the sense in which the book metaphor came to be applied in reasoning about the natural world and possibilities in scientific exploitation. We shall characterise this change as a partial shift of focus from the semantic (semiotic) to other aspects of the book and visible language as the donor subjects of the metaphor, such as the syntactic (rule-governed), perceptual (visual), and methodological. One essential element of the book metaphor which remained relatively constant before and after the transition was its objectivist implications. By this we mean the belief that there is a single correct way to read the "book of nature" existing independently of the human reader and fully external to him, and that scientific research amounts to discovering this objectively correct way of reading. 352

E.g. the parts of body were correlated with the zodiac and the movements of the celestial spheres determined favourable and unfavourable times for bloodletting. The shapes of some plants were interpreted as an indication of which diseased bodily organs could be cured using them, and, as we argue with Hutchinson (1987) in the section on Copernicanism, the configuration of celestial bodies allowed conclusions about the proper management of political structures.

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Some other assumptions, however, about what is a scientifically valid way to cognitively approach the object of research, underwent shifts in the transition from the Middle Ages and the Renaissance to the modem period. We shall indicate how some newly emergent philosophical ideas concerning this issue (subjectivity of sensual perception, secondary and primary qualities) found conceptual support in the book metaphor coupled with the spread of literacy in the age of printing. We wish to briefly consider several functions by which the metaphor of book and writing imparted an influence upon the development of modem physical science: • in all its implementations, expressing and stabilising the general idea of science as the reconstruction of the objectively given; • in its implementation as the Galilean metaphor of the mathematical alphabet of nature, which focused upon the combinatorial aspect of writing: - providing conceptual support for the mechanist philosophy, - providing conceptual support for the development of mathematical notation; • in its Baconian implementation as juxtaposition of "two books" - the Nature and the Scriptures: - enhancing the dignity of natural science relative to theology, - guiding the idea of establishing a basic corpus of natural knowledge. 5.3.1. The book metaphor and scientific objectivity 5.3.1.1. The independence of the text The absolute metaphor of the "book of nature" and its investigation as a process of reading, at first glance apparently merely decorative, in fact expresses and stabilises a certain general conception of the relation between the scientist - the human subject in search for the truth and nature as the object of investigation. Among the elements picked out from the book as the donor subject in the metaphor juxtaposing it with the world of nature, are: • the body of the text; • the intended reader; • the language and the writing system in which the text is written, the knowledge of which is a necessary condition for the ability of the reader to understand the message. Science is about 1) finding out which type of code (for example, morphographic, syllabographic, alphabetic) the world is written in, 2) identifying the particular elements (signs), 3) identifying meanings composed from the elements. This conceptualisation tends to stabilise • the objectivist belief in the existence of a pre-given, objectively valid "language of nature", whose rules are to be acquired and not, to any extent, invented, • the world picture in which natural processes are independent of the act of observation, the activity of the reader=cognising subject, just as the act of reading leaves the letters on the page of the book unchanged. The former issue has already been referred to in the section dealing with the metatheoretical views of contemporary physicists. With reference to the latter, it is to be noted that the picture of observation-independent facts was questioned in the context of the intro-

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auction of the uncertainty principle by Heisenberg in the 1920's. Nowadays, the influence of observation upon the processes under study is considered an important factor in quantum physics, dealing with processes taking place in very small dimensions. The possibility of a non-intervening observation is excluded even in principle. The measuring device interferes with the system in which the measurement is taken, changing some of its physical parameters;353 also, the measurement makes simultaneous observation of other aspects of the same phenomenon impossible.354 The extreme "objectivist" interpretation of this fact is that the very act of observation actually "destroys" some properties of the physical system, e.g. measuring the position of an elementary particle actually "destroys" its velocity, causing the expression "velocity of χ at the time y" to lack reference. The "constructionist" interpretation is to regard the representation including velocity of a particle and the representation including its position as mutually exclusive options and the principle of uncertainty as referring to a limitation on human knowledge, that is, a limitation on the possibility of translation from man-independent aspects of physical happening to their representation in the human mind. In any case, processes on the quantum level go different paths when different aspects of them are under observation; the conceiving subject and the object under study appear to form an inseparable entity. 5.3.1.2. Understanding as non-involvement: the reduction of observing to seeing Of vital importance for the changes in the book metaphor before and after the advent of modern physical science were the changes in the material circumstances of writing. The growth of literacy which followed the introduction of printing by Gutenberg in the first half of the 15th century meant a shift from an audio-oral to a visually oriented community. The widespread interiorisation of the visual medium of communication - the alphabet - altered the ratio in our senses, priming vision as the channel of information input and diminishing the significance of other channels; as a result, reading the book of nature became reading in a more visual sense, whereas previously it was much more that of decoding a message acquired by some kind of perceptual, cognitive, emotive mediation. For doing science, focusing upon the visual aspect means that the total immersion in the world of heterogeneous sensual stimuli is replaced by a withdrawal of the perceiving subject to the position of an observer from a distance. In modern times, emotionally disengaged observation from a distance is the way to conduct research into nature, different from earlier attitudes to nature such as magic or animism, which were based on a sort of a "direct" and holistic contact to the object of research. Paracelsus, the main representative of the Renaissance doctrine of signatures,355 used the book metaphor in his writings in the sense of things being signs invested with 555

E.g. the electron microscope used for observation in atomic dimensions operates through directing a beam of electrons into the system under observation and, thus, provides additional energy to this system. 354 Examples are the uncertainty principle, and the wave/particle duality of matter: we cannot observe both aspects in one experimental arrangement. J " that is, correspondences between different domains encodable from various indices, such as shape or colour similarity. According to the doctrine of signatures, "God hath imprinted upon the Plants, Herbs, and Flowers, as it were in Hieroglyphicks, the very signature of their Virtues", by which mainly their selective curative applicability was meant. Turner, quoted in Findlen 1990: 515.

175 multiple layers of meaning for the researcher to unravel and articulate.356 The language of his "book of nature" was allegorical and poetic, rather than strictly visual. Although it was mostly vision that communicated the existence of the correspondence, it did not mean the observer's withdrawal from the full sensory and spiritual immersion in the natural world. For Paracelsus, the world was full of disguised truths, and this was the way God displayed his power; they were attainable through a careful, spiritually informed reading of the book of nature.357 Signatures (visual similarities) provided the point of cognitive access, and experience was a necessary precondition; at the same time, 'Experience' in Paracelsian epistemology refers thus not merely to simple sensory familiarity, but to the cognitive identification with the object of knowledge achieved through insight.358 This is the opposite of rationalism based on the notion of the difference between the object of perception and its effect on the human subject, that is, of subjectivity of sensual perception. Whereas the Renaissance animistic-occultist conceptual frame stressed the cognitive identification with the object of perception as the condition of correct insight, rationalism recognised this "direct" contact as dependent on a complex cognitive mediation of the mind. The objective became to free oneself from the emotional and qualitative richness in order to receive the point of support for the true understanding and manipulation of Nature. This affective loss was experienced as an intellectual gain: it was enough to see nature in order to know her. Reading the book of nature became a matter of vision, not of empathy. And vision means detachment from the object under study because seeing is possible over a greater distance than any other kind of perception so that perceiving by seeing implies immersion in what is perceived to a lesser degree than any other kind of sense perception. The conception of the study of nature as reading provided conceptual support for this kind of sensory detachment.359 Sound, smell, and tactile impressions were eliminated from the physical world as secondary phenomena, mere products of perception itself. This reduction of investigation to one privileged sense hints at the reductionist trend in modern science: to explain everything through as little as possible. Summing up, while for the ancient and the Renaissance thinkers the "book of nature" is a book because it consists of signs possessing reference outside themselves, the metaphor of the book of nature in modern science - applied, in the period in question, first of all by Galileo - brings the feature "visual inspection" into the focus, allowing it to participate in the transfer as a central part of positive analogy. 356

357

358 359

Similarly to Plotinus, Paracelsus believes that "Just as a man reads a book on paper, so the physician is compelled to spell out the stars of the firmament in order to know his conclusions ... It is like a letter which has been sent to us from a hundred miles off, and in which the writer's mind speaks to us ..."Paracelsus 1922-25,9: 176. This holistic notion of "reading the book of nature", contrasting with Galileo's analytical, "alphabetic", strictly visualised notion is exemplified by the statement that "Whoever wishes to explore nature must tread her books with his feet ... Writing is learned from letters; Nature, however, [by travelling] from land to land; one land, one page. Thus is the Codex Naturae, thus must its leaves be turned." Paracelsus, quoted in Eamon 1994: 161. Wilson 1988: 91. Cf., however, section 4. 1. 3.. Because visual inspection is impossible in principle in some branches of modern physics, the "cognitive identification" with the object under study comes through the back door as an informal strategy of understanding via the self-projection of the researcher into a metaphorical world which "restores" the sensory availability of the objects represented.

176 The focusing on vision as the channel of acquiring knowledge of the world was supported by mathematisation of natural science. Rationalist philosophy accepts only the figure and dimension as the proper building blocks of reality, and mathematics at that time is realised largely in the form of geometry,360 so that the geometrical visualisation is part and parcel of the mathematisation of the world. As science becomes interested in the quantitative aspects of natural processes, vision becomes essential to the scientific reconstruction of the truth because vision is mathematical in view of its immediate link with geometry. 5.3.2. Alphabet of nature 5.3.2.1. Mathematical alphabet and mechanical philosophy It is in the works of Galileo that the transition from the mystical, semiotic sense of the book metaphor to its new function within rational physics can be observed at its fullest. In "Dialogue about Two Great Systems" (Journey II, the Second Day, 1967: 109), we read: I have a little book, much briefer than Aristotle and Ovid, in which is contained the whole of science, and with very little study one may form from it the most complete ideas. It is the alphabet, and no doubt anyone who can properly join and order this or that vowel and these or those consonants with one another can dig out of it the truest answers to every question, and draw from it instructions in all the arts and sciences. Just so does a painter, from the various simple colors placed separately upon his palette, by gathering a little of this with a bit of that and a trifle of the other, depict men, plants, buildings, birds, fishes, and in a word represent every visible object, without any eyes or feathers or scales or leaves or stones being on his palette. Indeed, it is necessary that none of the things imitated nor parts of them should actually be among the colors, if you want to be able to represent everything; if there were feathers, for instance, these would not do to depict anything but birds or feather dusters. A finite set of coloured paints combine to become representations of every possible object. The implied idea is that of "un Systeme combinatoire qui peut rendre compte de toute la multiplicite de l'univers".361 In a letter to Fortunio Liceti (Jan. 1641, 1966: 220), Galileo wrote: For me, to be true, I believe that the book of philosophy is the one constantly open before our eyes; but since it is written in characters different from those of our alphabet, they cannot be read by everyone; the characters of this book are no different from triangles, squares, circles, spheres, cones and other mathematical figures, perfectly suited to this reading. (Transl. HP.) The emphasis falls here upon the visual, geometric aspect of the elements of the alphabet in which the "book of philosophy", representing the world of nature "always open before our eyes", is written. The priming of vision, here stressed additionally by the fact that the concept of the alphabet is accompanied by the concept of painting, facilitated geometric spatialisation of concepts, providing support for a mathematical analysis of reality.

360

361

The sense in which mathematics was almost synonymous with geometry in the seventeenth century is explained in Burtt 1924, 1967. Briefly, solutions of mathematical problems were arrived at through their "translation" into configurations of geometrical figures and applying transformations to the latter. Thus, mathematics took a visual form. Calvino 1985: 686.

177 The quotation above is also a manifestation of another change in the donor subject of the book metaphor caused by the introduction of printing: the shift from an individually manufactured manuscript to a printed book. Whereas in a manuscript each letter was individually produced and slightly different from other specimens of the same sign, a printed book is based on the "typographic principle" described by Brekle (1997) as "ein wegen der eindeutigen physikalisch geregelten Abbildungsbedingungen besonders klarer Fall der allgemeineren Typ-Exemplar (type-token)-Relation", underlying any kind of mechanical production in general. The typographic principle incorporates, in the specific domain of visible language, the more general idea of a sub-set of a finite set of material elements which are used repeatedly, each time in new combinations, to create an infinite variety of possible structures (cf. Brekle 1997). In the age of printing, the book metaphor emphasises the idea of repetitiveness and combinatorics combining elements from a small finite set to an infinite richness of possible texts, open but governed by rules. By this, the emphasis in the comparison shifts away from the semiotic aspect of the language in which the book is written: the message to be decoded, to the technical and structural, combinatorial aspect of the visual language. Whereas in antiquity and the Middle Ages the book metaphor picked out referentiality and transferred this aspect of the visible language to the recipient subject, for Galileo, the world is like visible language because it consists of a fixed set of figures (alphabet) which are combined according to a fixed set of rules (syntax) to form a structure. This was akin to the ideas of mechanical philosophy in view of the similarity of the operating principle: the idea of a mechanism is also that of an aggregate of parts and rules for their operation, both closed sets but combinable into infinite richness of the visible world. An essentially similar, syntactic concept of the alphabet of nature focusing on the relation between simple and more complex forms and brought into association with geometry and mathematics appears some time later in Hooke's "Micrographia" (1665: 22): As in geometry, the most natural way of beginning is from a Mathematical point; so is the same method in Observations and Natural history the most genuine, simple, and instructive. We must first endeavour to make letters, and draw single strokes true, before we venture to write whole Sentences, or to draw large Pictures. ... [it is] difficult to explicate this configuration of Mushroms, without the previous consideration of the form of Salts; so will the enquiry into the forms of Vegetables be no less, if not much more difficult, without the fore-knowledge of the forms of Mushrooms, these several Enquiries having no less dependence one upon another than any select number of Propositions in Mathematical Elements may be made to have. Nor do I imagine that the skips from the one to another will be found very great, if beginning from fluidity, or body without any form, we descend gradually, till we arrive at the highest form of a bruite Animal's Soul, making the steps of our Enquiry, Fluidity, Orbiculation, Fixation, Angularization, or Crystalization, Germination or Ebullition, Vegetation, Plant Animation, Animation, Sensation, Imagination.3*2 (italics in original) The alphabet and language on the one hand, geometry and mathematics on the other appear to Hooke to be closely analogous. What makes them similar is their possessing a "syntax": rules for passing from simpler to more complex forms up to extreme degrees of complexity.

362

Hooke 1665, 1961: 127.

178 In acquiring knowledge of these rules and elements, one would be able to explain all the richness of the natural world pointing back to the underlying (simpler) level of structure. Reading the book of nature in the seventeenth century is done not by decoding hidden (encoded) references pointing outside this domain, but by acquiring knowledge of it through an analysis in terms of more and more elementary levels of structure, reaching ultimately its most elementary constitutive elements, the letters. There is an obvious affinity of this conception with mechanical philosophy, which Hooke frequently explicitly refers to in his work. 5.3.2.2. Alphabet of nature and mathematical notation The Galilean alphabet metaphor emphasises the visual aspect and removes the emphasis from the referential aspect of visible language. In this way, the notion of the book of nature seems to have had some influence upon the development of mathematical notation - the algorithm, which is not a transcription of the natural language but belongs to a coherent, selfcontained system, making possible the manipulation of symbols on an abstract level liberated from reference to the "givens" in the world outside. The images of the world as visible language on the one hand, and as mathematical on the other meet in the fragment already quoted from the letter to Liceti (cf. page 176): ... the book of nature is the one which is always open before our eyes ... its letters are no other than triangles, squares, circles, spheres and other mathematical figures ... In this statement, mathematics (geometry) and language (alphabet) approximate each other because both represent the constitution of the physical world. We can view this encounter of the ideas of visual alphabet and of mathematical description as conceptually facilitating the development of the system of mathematical notation. Prerequisite to this encounter was the priming of vision as the input channel, which de-emphasised the secondary character of writing, the notion of visible language as a reflex of speech. In the book-alphabet metaphor the connection between oral and visible language is of no interest. As the notion of writing as notation for speech is not included in the transfer, the metaphor rather loosens the association of visible language with speech. In this way, it helps pave the way for the development of a system of mathematical notation fully independent of the spoken language, a purely visual system in which signs are designed primarily for silent contemplation and not for phonetic realisation (cf. Alunni 1982). 5.3.3. Bacon's metaphor of two books 5.3.3.1. The dignity of natural knowledge Francis Bacon, a founding father of modern natural science and one of the most influential thinkers of the scientific revolution, put the book metaphor to use, reflecting upon the issue of the position of natural knowledge within the framework of knowledge in general. In "The Advancement of Learning", a highly influential piece of philosophising on moral and "natural" matters, the book of nature appears in close association with the book of God's word - the Bible. The parallel between the two domains of knowledge is already hinted at in the title, advertising "The Two Bookes of Francis Bacon of the Proficience and Advancement of Learning divine and humane". In the text of the treaties, we read:

179 ... let no man, upon a weak conceit of sobriety or an ill-applied moderation, think or maintain that a man can search too far or to be too well studied in the book of God's word or in the book of God's works: divinity or philosophy.363 Here, the two books: the Bible and the metaphorical book of nature appear beside each other, mentioned in one breath, and, as argued by Durel (1987: 380), this proximity is instrumental for enhancing the dignity of the secular pursuit of natural knowledge: ... l'existence d'une teile relation entre les deux livres implique en bonne logique que Γόη ait eleve la connaissance de la nature une dignite comparable celle du savoir revele. Bacon (1857-1874,3: 301) goes even further in the act of proximising the two books and endowing the natural knowledge with dignity reserved till then for the sacred truths of religion: ... our Saviour saith, You err, not knowing the Scriptures, nor the power of God; laying before us two books or two volumes to study, if we will be secured from error; first the Scriptures, revealing the will of God, and then the creatures, expressing his power ... the latter [= the book of nature] is a key to the former [=the Bible] ... chiefly opening our belief, in drawing us into a due meditation of the omnipotence of God, which is chiefly signed and engraven upon his works. Christ is speaking of God's power to resurrect the dead in accordance to the Scriptures. Bacon, on his side, dissociates the scriptures and the power of God, identifying the latter with the power of creation, and, consequently, nature. As a book revealing the power of God, nature acquires a prestige equal to that of the Bible revealing God's will. "On est done en droit de se demander s'il y a eu devaluation des valeurs spirituelles ou devaluation des valeurs scientifiques."36* At any rate, by means of the metaphor of the book of nature the two "valeurs" come closer to each other; there is a "relative movement" between them which marks an initial impulse directed towards what by now has become the overwhelming authority of science. 5.3.3.2. The "Authorised Version" of the Bible and Bacon's methodological thought A further thesis of Durel's concerning the guiding role of the book metaphor for the methodological thought in Bacon is that he was inspired by biblical exegesis to approach nature as a text to be interpreted. In 1611, the "Authorised Version" of the Bible was produced, "translated out of original tongues and with the former translations diligently compared and revised". Bacon thought it proper that the same method be applied to secular science: reducing the proliferation of commentaries hanging on the original body of the text. The new translation of the Bible integrates the multiple previous versions through comparison and revision, and this inspires Bacon in his vision of creating science which would assimilate the knowledge of the ancients while at the same time making them redundant. His ideal programme is to reduce redundancy in natural knowledge by procuring the true text.

363

364

Bacon 1857-1874,3: 268. What Bacon is referring to is the misinterpretation of the fragment from the Epistle to the Romans (11: 20), containing a warning against moral pride, as a warning against intellectual knowledge. The misinterpretation was based on a misleading Latin translation of the original text and, being widespread in the Middle Ages and early Renaissance, constituted an argument for those objecting to the pursuit of knowledge cf, for example, Ginzburg 1976. Durel 1987: 382.

180 For Bacon, one should, by diligent action, arrive at the compact "original" instead of proliferating books: ... the opinion of plenty is among the causes of want, and the great quantity of books maketh a shew rather of superfluity than lack; which surcharge nevertheless is not to be remedied by making no more books, but by making more good books, which, like the serpent of Moses, might devour the serpents of the enchanters.363 Bacon holds it to be advisable to make a list of "terrae incognitae" and subjects which have already been treated by natural philosophers; if one could produce such a summary of the existing body of knowledge, excluding all repetitions, it would be a significant step towards the acquisition of knowledge. In MacLuhan's (1969: 223) formulation, Bacon took the lesson of print to be that we could now literally get Nature out in a new and improved edition.

365

Bacon 1857-1874,3: 327-328.

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6. Stipulative reference extension

In contrast to world theories and to special purpose adaptations of ubiquitous "underlying metaphors" taken over from general language and cognition, metaphorical processes which we call stipulative extensions of reference and which also produce physical concepts and lexicalised terms to express them are more restricted in their scope and specific to physical theory. They originate in the context of physical research as a result of an explicit recognition of similarity between two entities (things, events, processes) described by physical theory. We characterised a stipulative extension of reference as a process in which a hypothesis rightly assuming (not overstating) a theoretically significant physical similarity between two subjects leads to the transfer of language from the familiar to the less familiar; and in which this initial hypothesis becomes confirmed by the later growth of knowledge so that the domains involved are amalgamated into one category, which is accompanied by stabilisation, in usage as well as by formal physical definition, of the restructured meaning. At the first application of the denotation of a scientific concept with extended reference, the similarity constituting the ground of transfer is explicitly defined and assumed to be significant from the point of view of the theory which applies to the phenomena under consideration. Instances of stipulative reference extension are the application of the word "wave" by Huygens to the way of sound propagation, and the process which gave physical and linguistic significance to the concept of "invisible light", two hundred years ago an oxymoron which could only be used metaphorically (e.g. to express spiritual experience of enlightenment), today a literal expression of metaphorical origin.

6.1. Stipulation of meaning: Huygens' notion of sound wave The first stage of the metaphorical history of the wave concept, discussed in the following section as an instance of assimilative metaphor, was a stipulative extension of reference of the word "wave" by Huygens in "Traite de Lumiere" (1690). Originally, "wave" denoted waves on the surface of a fluid induced by a mechanical disturbance. Huygens (1690, 1952: 554) applied it to the way sound spreads in the air: We know that by means of the air, which is an invisible and impalpable body, sound spreads around the spot where it has been produced by a movement which is passed on successively from one part of the air to another; and that the spreading of this movement, taking place rapidly on all sides, ought to form spherical surfaces ever enlarging and which strike our ears. Now there is no doubt that all that light also comes from the luminous body to our eyes by some movement impressed on the matter which is between the two; since, as we have already seen, it cannot be by the transport of a body which passes from one to the other. If, in addition, light takes time for its passage ... it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as sound does, by spherical surfaces and waves; for I call them waves from their resemblance to those that are seen to be formed in water when a stone is thrown into it, and which present a successive spreading as circles, though they arise from another cause, and are only flat in surface, (emphasis HP)

Here, Huygens names explicitly "spreading as circles" as the ground of the meaning extension of the word "wave" to the mechanism of sound propagation; implicitly, he is hinting

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at the propagation by regular (oscillatory) motion of particles passed from one to another by mechanical contact. This is an act of a stipulation of meaning referred to by Rothbart (1984: 609) in which a word becomes applied in an unusual context which is followed by an immediate lexicalisation of the new, in this case generalised, meaning. The ground of the meaning transfer is highlighted and becomes more salient as a meaning component of the notion of a wave, other usual components of donor subject or the parent situation - such as, for example, wetness and foam and the observable sinusoidal shape of the fluid - are relegated to the margin. The stipulative metaphor is "dead" on the spot.

6.2. Invisible light and Roentgen's "invisible rays" The notions "light" and "ray" were originally used to refer to visible light, whose reference has been extended to phenomena not involving visible light, such as the electromagnetic waves in the ultra-violet and infra-red part of the light spectrum, X-rays, and the radioactive radiation. The extension of meaning came gradually. The first step in it was the report on the discovery of "invisible rays" of light beyond the violet end of the light spectrum by Ritter (1801: 527). Ritter's claim about the existence of such rays was based on the observation of the chemical effects caused by them same as the effects of visible light (blackening chloride of silver). Later, Young demonstrated that they show interference like visible light. Thus, the notion of "light" was extended in such a way that the visibility of the agent became marginalised as the components of their meanings and other properties of light rays, such as their effect on chemical substances and interference, moved closer to the centre. Today, we speak of invisible light (ultraviolet, infrared light) without contradiction. Meanwhile, the hypothesis expressed by the use of "light" to refer to the effects observed by Ritter has become a highly confirmed theory. The agent of the observed changes and visible light turned out to be describable as different parts of the same continuum: as electromagnetic waves of different frequency ranges. The similarities which motivated the new language use turned out to be significant aspects of physical reality as it is explained by the theory of electromagnetism. According to Czucka (1988) and Czucka (1993), a similar change affected the word "ray" on its way from optical phenomena to X-rays (and other kinds of more recently discovered radiation) after Wilhelms Roentgen's discovery of the latter. The story of the notion of a ray, however, is more complex. At first applied in optics, already in the 18th century "ray" signified not only visible light rays but also other phenomena characterised by properties such as propagation in straight lines and reflection or fading out at obstacles, and was also a geometrical notion. With Roentgen's description of his discovery in 1895, its reference was extended to cover the new agent. Roentgen observed and described the phenomenon of "Schattenbildung" on a photographic plate placed behind a glass vessel containing a highly rarefied gas through which an electric current was passed, and an intervening solid object. He named the image on the photoplate a "shadow" (Schatten) of the intervening object, and came to the conclusion that the agent of the phenomenon came out of the sample and was propagated in straight lines. Because of this way of propagation, creating sharp "shadows" on the plate, and the fluorescence produced when the agent acted upon a fluorescence screen, he named the agent "Strahlen" (rays). According to Czucka, Roentgen was conscious of the

183 fact that he was creating a new language, as shown by the wording in which he announced his discovery in the original publication. He explicitly named the factors which led him to using the words "Strahl" and "Strahlung" as justifying the application of his descriptive terms: Die Berechtigung, für das von der Wand des Entladungsapparates ausgehende Agens den Namen „Strahlen" zu verwenden, leite ich zum Theil von der ganz regelmäßigen Schattenbildung her, die sich zeigt, wenn man zwischen den Apparat und den fluoreszierenden Schirm (oder die photographische Platte) mehr oder weniger durchlässige Körper bringt.3"

In Roentgens "Mittheilung", shadow is an image ("Abbild") of a thing caused by a physical agent whose source is situated behind the object opposite to the screen onto which the "shadow" is thrown. This involves a change in the semantics of "shadow", consisting in the decentralising of visible light as the component of meaning. Czucka (1985,1988) argues that in Roentgen, in the process of its extention to the new agent, "Strahl" also undergoes such a stretch of meaning. He quotes Mauthner (who was the first to posit the metaphorical character of Roentgen's terms) tracing the notion of "Strahl" back to its source in "einer veralteten Optik, welche sich die Lichtquelle gewissermaßen schießend dachte", from which it emerged through a metaphorical shift of meaning. For Czucka (1993: 43-44), "gerade einer solchen Vorstellung der ,alten Optik' nähert sich die ,Strahlenmetapher' bei Röntgen offenbar wieder an; so ginge es bei Röntgen ... um die Aktualisierung einer älteren metaphorischen Bedeutung in einer neuen Begrifflichkeit". However, the thesis of the radical newness of Roentgen's language use is not convincing, in view of the before mentioned applicability of the word "ray" on the basis of straight propagation and the behaviour at obstacles long before Roentgen's report. The concept of a ray seems not to have undergone any significant re-structuring of meaning (core/margin shifts) under Roentgen's treatment: it was a case of the application of a concept, rather than its extension.

Roentgen 1895: 11, quoted in Czucka 1988.

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7. Assimilative metaphor A kind of extended metaphor producing lexicalised "satellite metaphors" is what we call "assimilative metaphor". Assimilative metaphors are models which used to be held for actual mechanisms of processes they are models of. In contrast to the ubiquitous all-purpose extended metaphors which we called "underlying metaphors", they are constructs specific to scientific theory displaying its "discovery" aspect, combined with the gradual linguistic process of meaning change. Nonetheless, they may be related to ubiquitous "underlying metaphors" (e. g., we assume that the concept of wave could be extended to non-material referents owing to the existence of the underlying metaphor "change is movement"). We apply the name "assimilative metaphor" to a metaphor which is a product of a false hypothesis consisting in a false categorisation of a field of phenomena: an overstatement of an analogy between two sorts of physical processes. When such a hypothesis becomes abandoned after the error of categorisation has been acknowledged, some part of the associated conceptual network may still persist in the model-theoretical or educational function and linguistic usage. The old hypothesis functions then as a metaphorical model "spinning off" a matrix of terminology which remains in use. In contrast to stipulative metaphors based on the inventive transfer of denotations or sudden insights in the possibility of drawing structural parallels between two domains, the assimilative metaphor is a result of the adaptation of the existing concepts and labels to theory changes in view of which they turn out not to be literally applicable to the phenomena under investigation.

7.1. "Fluid" electricity In this section we analyse the development of the concepts of electricity, demonstrating what we claimed earlier in the section on the relationship between metaphor and false hypothesis - that the fluid theory of electricity was a non-metaphorical hypothesis; therefore, along the lines we have adopted, terms such as "electric current", "electric charge", "condenser", "electrical density", and the like retained by physical terminology can be talked of as metaphorical only after the fluid hypothesis has been abandoned. The language applied to the description of electrical phenomena seems to have gone more than a full circle. The stage at which terms such as "flow" and "transport" came to be used as a merely phenomenological description of observed processes gave way to the stage of the fluid theory of electricity which ascribed to them "factual" meaning as referring to the actual flow of an electrical substance. In the following stage, the theory was rejected or died a natural death and expressions such as "flow of electricity" regained their metaphorical status. At the same time as they were turning into satellite metaphors of an out-dated hypothesis, the process of the lexicalisation of their new senses ("death of a metaphor") was taking place. Their connotations of substantiality became reinforced once more as the electron hypothesis led to the model of the electric current as the continuous movement of tiny particles along the conductor line.

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7.1.1. The rise and the concepts of the fluid theory In section 4.1.1.2. we treated the process which led to the establishment of the notion of "electricity" denoting the agent of the observed effects of experiments with electrified objects. The first modern theory concerning the nature of this agent comes from William Gilbert, who thought that the cause of static electricity was a material substance imprisoned in glass or amber and liberated from them under the influence of friction, which excited this substance and made it issue from the body as an effluvium forming an "atmosphere" around it. The effluvium hypothesis found wide acceptance (its adherents were Niccolo Cabeo, Sir Kenelm Digby, Robert Boyle, and Wilhelm Jacob s'Gravesande, to name but a few). Newton, too, believed that the electrification of glass consists in the exhalation of vapours under the influence of heating through rubbing and their re-entry: "There is something of an aetheral nature condens'd in bodies". He described this substance as a "most subtle spirit which pervades and lies hid in all gross bodies".367 When he set off to answer the question how the all-pervading aether can be so rare as to provide no hindrance to the movement of the heavenly bodies, he argued by pointing to the existence of the electrical matter which remained active even if very rare: If any one would ask how a Medium can be so rare, let him ... tell me, how an electrick Body can by Friction emit an Exhalation so rare and subtile, and yet so potent, as by its emission to cause no sensible Diminution of the weight of the electrick Body, and to be expanded through a Sphere, whose Diameter is above two Feet, and yet to be able to agitate and carry up Leaf Copper .. .3"

The reason for static electricity, then, was identified as a substance and the whole phenomenon as mechanical in its nature. The next step in the theory of electricity came with the discovery of electrical conduction. As stated before (cf. section 4.1.1.2.), Gray, who, in 1729, published the results of his famous experiments on conduction and electrification by influence, spoke in his description of the electrical virtue passing and being conveyed or transported from one object to another along a conductor line. We stated that in this account, the notion of transporting or conveying of the "virtue" seems to be of a purely phenomenological character, that is, to involve no claims concerning the substantiality of the cause of the movement of small objects towards the ivory ball to which the "electric virtue" has been "passed" or "conveyed". The verbs of movement are applied here in a metaphorical way, in a sense neutral with respect to the issue whether the grammatical subject - "electric virtue" - has a substantial counterpart. In numerous later accounts of electrical phenomena, however, the grammatical subject of these verbs becomes associated with a material counterpart; that which "passes" and "returns" becomes not only conceptualised as a thing but also taken to be a thing - the electric fluid: ... the mechanistically minded scientists of the eighteenth century were prone to consider the transfer of a property from one object to a second as being due to the transfer of a substance. Thus a bucket that gets heavier presumably has had something weighty put in it; an object that gets hotter has had heat added to it; and, by analogy, an object becomes electrified because some electricity is added to it. Thus soon after Gray's work the term 'electricity' rather quickly comes to have a meaning of a substance within - or perhaps on the surface of- an electrified object. This substance is invisible, but postulation of its existence offers a reasonable explanation of electrification by *" Newton: Principles. Scholium Generale. 1952: 372. *" Newton, Isaac: Opticks. Query 22. 1952: 522.

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contact: an object electrified by rubbing contains this invisible electricity, and when it touches an unelectrified object some of the electricity is transferred. The ease of transfer from one object, directly or through a string or other intermediary, to a second led to the view that this easily flowing electricity was a fluid, and was often called the 'electric fluid'...3" In what follows we have a look at the properties attributed to the electric fluid and show that they were all included in the standard sense of the notion of a fluid. This we take to mean that the application of this concept to the electrical phenomena involved no significant change of meaning (violation of its initial semantic restrictions), but merely a change in the extension of the concept, which does not constitute a metaphor but a literal application to a new instance. The word "fluid" was first used as a noun in English by Boyle. The Cartesians defined a fluid as a substance whose minute parts are in a constant agitation. Johnson's Dictionary (1836) lists the adjective "fluid" as "having parts easily separable; not solid", quoting from Newton: If particles slip easily, and are of a fit size to be agitated by heat, and the heat is big enough to keep them in agitation, the body is fluid; and if it be apt to stick to things, it is humid. The noun "fluid" is defined as "any thing not solid", and for "fluidity" we read: The quality of bodies opposite to stability; want of coherence between the parts, followed by a quotation from Newton: Heat promotes fluidity very much, by diminishing the tenacity of bodies; it makes many bodies fluid, which are not fluid in cold, and increases the fluidity of tenacious liquids; as of oil, balsam, and honey; and thereby decreases their resistance. The term "electric current", referring to the flowing electrical fluid, has been in use since the mid-eighteenth century.370 The term "electric stream" was alternatively used,371 but gradually went out of circulation. After Gray's discoveries it was no longer possible to believe, as had been universally believed before, that the electric effluvia were inseparably connected with the bodies from which they were evoked by friction. Accordingly we find them recognised, under the name of the electric fluid, as one of the substances of which the world is constituted. The imponderability of this fluid did not... prevent its admission by the side of light and caloric into the list of chemical elements."2 Till the discoveries of Lavoisier in the second half of the eighteen century, ponderability was not a necessary condition of substantiality: ... to postulate the existence of matter not subject to gravitation would be heretical today, of course, but this was no means in the eighteenth century, when Newton's law of gravitation had yet to be firmly established .. ."J

3

" Roller and Roller 1954: 47-48. Cf., for example, Gentleman's Magazine XVII, 1747: 141; Franklin 1752, 1887: 253. Quoted in O.E.D., 2nd edition. 371 Cf, for example, Philosophical Magazine IV, 1799: 59, 163, 309. 372 Whittaker 1973: 42. 373 Home 1981:95. 370

187 A chemical element such as light, heat, and aether, the agent of electricity was a fluid material substance sharing essential properties with other fluids. The effluvial theory regarded attraction and repulsion as mechanical effects of movements of this material substance. Digby, speaking of static electricity, says of the return of the electrical effluvium back into its source (an electrified object), which he takes to be the reason of the electrical attraction, that it is "like the condensation of a vapour by cooling", and speaks of "electric matter" (cf. Whittaker 1973). C. F. du Fay (1981: 52) speaks of "la matiere electrique" and "les ecoulements electriques" running along the conductor lines; Nollet (1743, 1981: 107) uses the expression "la matiere electrique" arguing that "on peut... presumer que I'electricite est 1'action d'une matiere en mouvement entre le corps electrise et celui sur lequel il exerce ses impressions". Among his arguments for the existence of this matter were that it could be smelled (as the odour produced in some electrical experiments) and seen (as a stream of light leaving a metal wire brought near to a rubbed globe producing static electricity). Galvani, having discovered the phenomenon of muscular contractions of vivisected animals coming in contact with metallic bodies, which soon became known as Galvanism or Animal Electricity, believed that he had actually observed "that a kind of circuit of subtle nervous fluid (resembling the electric circuit which is manifested in the Leyden jar experiment) is completed from the nerves to the muscles when the contractions are produced".374 He believed that this fluid was a substance of the same sort as "common electric vapour".375 The electrical substance was believed to be palpable, after what is called now "electric wind" (the tinkling sensation felt when an electrified body is brought near to the human skin) had been described by Hauksbee. Newton states that It appears that a cylindrical rod of glass or hard wax strongly rubbed emits an electric spirit or vapour which pushes against the hand or face so as to be felt ..."* And according to a report of the French Academy of Science, Around an electrified body there is formed a vortex of exceedingly fine matter in a state of agitation, which urges towards the body such light substances as lie within its sphere of activity. The existence of this vortex is more than mere conjecture; for when an electrified body is brought close to the face it causes a sensation like that of encountering a cobweb.177 The fluid hypothesis had such a grasp upon the minds of those engaged in the experimental work on electricity that it inspired them to conceive of bottling it; the early form of electric condenser, invented independently by Kleist and Musschenbroek in 1840's, was that of a flask, which device came to be known as a Leyden (Leiden) jar. 374

Galvani 1791: 377, quoted in Whittaker 1973: 68. In the original Latin text, we read: "Utramque autem auxit tenuissimi fluidi nervei circuitus veluti quidam, quem a nervis ad musculos ... phaenomenon contingeret, fieri, atque ad electricum circuitum, qui in leidensi phiala absolvitur, accedere, casu animadvertissimus" (1894: 75). Von Oettingen translated it into German: "Wir wurden in beiderlei Hinsicht bestärkt durch die Annahme eines sehr feinen Nervenfluidums, das während der Erscheinung von den Nerven zu den Muskeln fließe, ähnlich dem elektrischen Strome in der Leydener Flasche" (ibid.: 23). Whittaker prefers to interprete "animadvertimus" as "observe", which is also more consistent with the preceding text. 375 which he identified with fire, a fluid substance of specific properties; this hypothesis enjoyed some popularity in the mid-eighteenth century leading many researchers to speak, literally, of the "electric fire" instead of the electric fluid. The material view of fire, which had its origins in the traditional chemistry of the seventeenth century, described air and fire side by side as elastic fluids. "' Newton, unpublished draft, quoted in Home 1992: 198. 177 Histoire et memoires de Academic Royale des Sciences 1733: 6, quoted in Whittaker 1973,2: 43.

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Franklin believed that the electrical fluid, for which "common matter is a kind of sponge",378 consisted of particles extremely subtile, since it can permeate common matter, even the densest metals, with such an ease and freedom as not to receive any perceptible resistance."9 It was repulsive of its own particles like other elastic fluids: Electrical matter differs from common matter in this, that the parts of the latter mutually attract, those of the former mutually repel each other ...J8° Franklin speaks of this property as differentiating the electrical matter from the common matter, but the same property was assumed to characterise other fluids, such as air, Newton having shown that Boyle's law can be derived from such an assumption. This property of fluids was regarded to constitute their elasticity; Whittaker (1973) defines the adjective "elastic" used of fluids in the eighteenth century as "repulsive of their own particles". Similarly, Watson (1745: 485) says: "In electrified bodies, you see a perpetual Endavour to get rid off their Electricity", which meant that, in eighteenth century terms, electricity was an elastic fluid whose particles repelled each other so that, whenever possible, the excess electrical matter would be driven off an electrified body. The electric spirit of the effluvial theory as well as the communicable electrical fluid of the later stage had a certain density and could be condensed or rarefied: Now whence all these irregular motions should spring I cannot imagine, unless from some kind of subtill matter lying condens'd in the glass, & rarefied by rubbing as water is rarefied into Vapour by heat, & in that rarefaction diffused through the Space round the glasse to a great distance, & made to move & circulate variously & accordingly to actuate the papers, till it returne into the glasse againe & be recondensed there ... this condensed matter by rarefaction into an aetheral wind (for by its easy penetrating & circulating through Glass I esteeme it aetheral) may cause these odd motions, & by condensing againe may cause electricall attraction ..."' Some decades later, Watson (1746: 718) believed that he had shown that electricity is the effect of a very subtil and elastic fluid, occupying all bodies in contact with the terraneous globe ... under certain circumstances, it was possible to render the electricity in some bodies more rare than it naturally is, and, by communicating this to other bodies, to give them an additional quantity, and make their electricity more dense, (emphasis HP) Watson uses the expression "electric current" to denote the flow of electrical matter set in circulation by friction and uses an analogy with the blood circulation in an animal body: ... so that here the office of the Globes exactly tallies with that of the Heart in Animals; which, as long as the Quantity of Blood is supplied, propels it into the Arteries, and these all over the System; or that of the Pump in Hydrostatics. In the same manner, by the Attrition of glass Tubes, the electrical Power is brought from the Body of the Man who rubs the Tube; and he is constantly taking in a supply from the Floor.382

378 379 580 381 382

Franklin, quoted in Whittaker 1973,1: 49. Franklin 1941:213. ibid. Newton 1959,1: 365. ibid.

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Coulomb (1788: 561; 1973: 58), who supports the two-fluid theory of electricity ("resinous" and "vitrinous", or "plus" and "minus" electricity being effects of two different electric fluids), explains the "two kinds" of electricity, assuming literally that particles of the same fluid repel each other, and those of two different fluids attract each other in the same way as the gases whose particles repel each other, but are attracted by particles of the complementary gas: The supposition of two fluids is moreover in accord with all those discoveries of modern chemists and physicists, which have made known to us various pairs of gases whose elasticity is destroyed by their admixture in certain proportions - an effect which could not take place without something equivalent to a repulsion between the parts of the same |;as, which is the cause of its elasticity, and an attraction between the parts of different gases, which accounts for the loss of elasticity on combination.

Moreover, the absence of the characteristic properties of the opposite electricities when in combination was sometimes further compared to the neutrality manifested by the compound of an acid and an alkali (cf. Whittaker 1973: 58). Summing up, the hypothetical electric fluid shared with other fluids all their significant properties such as • particle structure, • mutual repulsion between its particles as the cause of its elasticity, and, in two-fluids theory, mutual attraction between the particles of and neutralisation of complementary fluids, • density, • palpability, • smell, • (possibly) visibility. Completely in accordance with the electrical substance hypothesis, the following questions were made the subject of an award in 1803 by the Batavian Society of Sciences in Utrecht: Wie ist die elektrische Materie beschaffen? Ist sie zusammengesetzt? Was hat sie für Bestandtheile? Was für chemische Veränderungen leidet sie, indem sie sich mit anderen Körpern vereinigt, und was für Veränderungen bringt sie in diesen Körpern hervor? "

In an article on electricity in Gehler's "Wörterbuch der Physik" in 1827, Pfaff lists several hypotheses concerning the chemical nature of electrical matter. Some supporters of the onefluid theory of electricity identified it with "imponderables" such as phlogiston, fire, and heat, all of which were supposed to be chemical substances; others identified them with chemical substances in the contemporary sense of the word. J. F. Mayer (1770) thought that the electrical matter was composed mainly of acids; Deliic (1787) believed that it belonged properly to the physical category of vapours and compared it to water steam to demonstrate that it manifested all the typical physical properties of vapours, explaining some electrical phenomena as resulting from these properties. Among the supporters of the two-fluid theory of electricity, Wilke identified the two fluids with fire and acid (cf. Gehler 1827,3: 352), Kratzenstein saw in them phlogiston and acid (cf. ibid.: 353), Karsten believed they were identical with air saturated with fire and phlogiston bound to a weak acid (cf. ibid.).

Quoted in Heideiberer 1979: 37.

190 In accordance with the hypothesis of a substance as the agent of electricity, the act of electrification ... came to be regarded as one of filling an object with an electrical fluid, which by analogy with the act of loading or charging something - such as a cannon with gunpowder - came to be called 'charging'.'84 "Charge" means primarily a load or burden, the quantity of substance, e.g. fuel, held by a container or apparatus. Like the electric stream or current, "electric charge" is not an object, directly perceived, but an attribute we have invented because there is something different about rods before and after rubbing; we say that the charges are alike because we have performed similar physical operations on like materials. However, the fluid theory of electricity endowed the notion of the electric charge with substantiality which turned it from mere nominalisation of "charging" as an act resulting in certain observable processes into a substance acting as an agent in these processes. Another term from the same network of concepts is "electric capacity". Originally, capacity referred to the ability of a receptacle to contain a quantity of substance. It was used in this sense to talk of electricity and its "storage" in its "receptacles": The celebrated Father Beccaria supposes that the action of rubbing increaseth the capacity of the Electric, i.e. renders the part of the Electric, which is actually under the rubber capable of containing a greater quantity of electric fluid.185 Of the same origin is the term "condenser", meaning generally "that which makes dense, collects into smaller space".386 Johnson's dictionary (1755, 1836) defined the verb "condense" as "to make any body more thick, close, and weighty; to drive or attract the parts of any body nearer to each other". In 1792, Volta wrote: ... the metal plate ... does actually condense or acquire a greater quantity of electricity.387 [...]! had rather call it a condenser of electricity ... using a word which expresses at once the reason and the cause of the phenomena.388 Similarly, the term "resistance", physically defined by Hobbes (1656, 1989,1: 211) as "the endavour of one moved body ... contrary to the endavour of another moved body", was initially applied to the electric resistance in the usual mechanical sense of a resistance offered by one body to the pressure or movement or another; it belongs conceptually to the picture of a fluid moving within a conductor line. Also "electric density" was originally associated with the idea of storage of the material electrical fluid. 7.1.2. Re-definition of substance and the abandonment of the fluid theory In 1775, Lavoisier enunciated the principle of the conservation of mass: the total weight of the substances participating in chemical reactions is the same before and after a reaction. As soon as the principle comes to be universally applied, ponderability begins to assume the status of a criterion of substantiality: it becomes added to the central meaning components 384 385 386 387 388

ibid.: 48. Cavallo 1777,2: 103. O.E.D., 2nd edition. Volta 1782: 245. ibid., App. 8.

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of the concept of substance (and, implicitly, that of a fluid as a sub-category of substance). As a result of Lavoisier's discovery, light and heat parted company from the elements in the scheme of chemistry. The structure of the category changed as a result of a scientific discovery; the criteria for being a "proper" member of it were now different. The change did not come unresisted. Fleck (1935, 1983: 58) quotes Jacob Reinbold Spielmann (Institutiones chemiae praelectionibus academicis adcommodatae. Argentorati, 1763), who "in jenem Zeitpunkte mit Recht jeden Schluß aus Gewichtverlust verneinte, ,da bis jetzt die wahre Ursache der Schwere den Physikern noch unbekannt ist'"; Lavoisier, though, introduced weight as a self-evident factor, without theoretical justification. As late as in the early 19th century Berzelius (quoted in Whittaker 1973: 80) could still argue that it would be wrong to grant the title of matter to ponderable things only, excluding heat and electricity from the class of material things; such an application of the term seems to him too narrow. He points out that electricity behaves as matter, perforating an object (non-conductor) put in its course: It, indeed, passes through conductors without leaving any trace of its passage; but it penetrates nonconductors which oppose its course, and makes a perforation precisely of the same description as would have been made by something which had need of place for its passage. And in a German article on electricity which appeared as late as 1827, we read: Es scheint mir zuvörderst ganz ausgemacht zu seyn, daß den ei Erscheinungen ein eigenthümliche Materie, die zu den ätherischen Flüssigkeiten zu recnnen ist, zum Grunde liege. Auf dem Standpunkt der dynamischen Physik, auf welchen Oersted in seiner Theorie sich befindet, wüdre freilich diese Materie in ein blosses Spiel von Kräften sich auflösen, jedoch in keinem ändern Sinne, als gleichfalls jede andere Materie. Indem ich also der E. ihre Materie vindicire, soll weiter nichts behauptet werden, als dass sie einen Bestand für sich hübe, dass sie also nicht in einer blossen besondern Thätigkeit der ponderablen Körper, etwa in einjr eigenthümlichen zitternden Bewegung derselben besteghe. Der Beweis hiervon liegt unwidersprechlich darin, dass die Fortpflanzung dieser Thätigkeit durch einnen Raum um so leichter und ungehinderter statt findet, jemehr er sich der vollkommenen Leere nähert. Da es also an einem anderweitigen Träger dieser Thätigkeit fehlt, so muss sie ihn selbst mit sich bringen, d. h. die E. hat eigenthümlichen materiellen Bestand.™ (italics in original)

At about the same time, however, the reality status of the "electric current" no longer appeared necessary to those who agreed to use the expression. In his early works in the early decades of the 19th century, Oersted already spoke of electric cuiTent without any reference to electric fluid (cf. Oersted 1850-51); Grove (1846: 48) stated that From the manner in which the peculiar force called eleciicity is seemingly transmitted through certain bodies ... the term current is commonly used to denote its apparent cause, (emphasis HP) Faraday (1882, 1965: 513) remarked: Whether there are two fluids or one, or any fluid of electricity, or such a thing as may rightly be called a current; still there are well-established electric conditions and effects which the words "static", "dynamic" and "current" are generally employed to express; and with this reservation they express them as well as any other.

The theory change which led to the exclusion of the electric current from the class of fluid substances did not mean merely that the boundaries of the category changed, but also that a "» Gehler 1827: 382.

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whole set of associated properties, like the corpuscular structure and with it the mutual repulsion between the particles of "electric matter" etc., became dissociated from the notion of the electricity; other properties, on the other hand, could only be attributed to it now in changed, metaphorical senses, such as possessing a certain "density" and being susceptible to "rarefaction" and "condensation". "Density" was soon defined as the ratio of mass to volume, and the term "electrical density" as the ratio of electrical charge to volume. Thus, "density" has undergone a split into two senses - separate on the level of theory and definition, but retaining some amount of conceptual association. "Electric density" turned to a satellite metaphor of the metaphorical conceptualisation of electrical phenomena in terms of material substance, just as happened with the terms "electric charge", "electric resistance", "condenser", "electric capacity", "electric current", used previously in a literal sense and retained in the terminology after the fluid theory was abandoned. 7.1.3. Flow of electricity and the electron theory Owing to the development the electron theory, the notion of the electric current regained some of its original visualisability and substantiality in the image of a stream of tiny particles "flowing" along the conductor line. Poincare (1902, 1968: 176) speaks in this context of a "rebirth" of electric fluids: "les fluides de Coulomb ... reparaissent sous le nom d'electrons". However, the current of electrons and the electric current are two different notions: the velocity of the electron flow is an altogether different matter than the velocity with which its observable effects, i.e. the "electric current", spread - the latter is the velocity of the electric field (electromagnetic waves). The stream of electrons, then, is not to be identified with the electric current, which is the word used to refer to the observable effects of an electromagnetic field spreading along a conductor of electricity. 7.1.4. Flow of electricity as educational analogy Today, the "flowing fluid" analogy is sometimes used for educational purposes, as in the introduction to electricity by Koff (1961: 100): The idea that electricity flows as water is a good analogy. Picture the wires as pipes carrying water ... Your wall plug is a high-pressure source which you can tap simply by inserting a plug ... A valve (switch) is used to start or stop flow.

The educational analogy "electricity=fluid flow" is meant to convey a system of relationships which can be imported from hydraulics to electricity, e.g. to explain the effects of serial or parallel junction of electric batteries or to clarify the interrelation between current, voltage and resistance, having its equivalent in hydraulics. It has been demonstrated that it actually has a facilitating effect in reasoning about electric phenomena (cf. Gentner and Gentner 1983).

7.2. The concept of wave Another notion whose history includes a transition from literal to metaphorical in its application to the same referents is the notion of wave. As shown in the preceding section, in

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the case of electrical phenomena, the assimilation of language to new recognitions proceeded by the establishment of new concepts polysemous with the old ones. The history of wave concept exemplifies the other kind of assimilative adaptation of theory and language: here, the assimilation making possible the retainment of the existing references (extensions) of words proceedes through restructuring meaning. 7.2.1. The aether waves: mechanical similarity of light and sound When, in "Traite de Lumiere" (1690,1952: 554), Huygens applied the word "wave" to denote the way in which sound spreads in the air (producing a stipulative metaphor discussed on page 188), he also put forward the hypothesis that it constitutes the mechanism of the light propagation: It is inconceivable to doubt that light consists in the motion of some sort of matter ... When one considers the extreme speed with which light spreads on any side, and how, when it comes from different regions, the rays traverse one another without hindrance, one may well understand that... it cannot be by any transport of matter coming to us from this object... It is then in some other way that light spreads; and that which can lead us to comprehend it is the knowledge we have of the spreading of sound in the air.

The early theory of light as oscillatory or "wave" motion, associated with such names as Hooke, Bernoulli, and Euler, was based on the hypothesis of literal similarity of the mechanism of light and sound processes, consisting in generic identity of the objects involved and their mechanical properties. According to this hypothesis, light was propagated by waves of corporeal aether. The aether was assumed to be a fluid substance acting as a carrier of light due to the same structure and mechanical properties which made air the carrier of sound. The following quotation from Euler (1769, 1986)390 demonstrates to what extent the similarity between sound and light was assumed to hold by the proponents of the wave theory of light. It shows that taking sound as a model for light was meant to explain the "real mechanism" of light production and propagation. The hypothetical similarity concerned not only the general principles governing its operation but also more specifically the mechanical properties of the physical carriers of both sensations: Diese feine Materie, die den ganzen Himmelsraum zwischen den himmlischen Körpern einnimmt, ist der Aether, dessen äußerste Feinheit nicht in Zweifel gezogen werden kann ... Der Aether ist... eine flüssige Materie wie Luft, aber unendlich viel feiner und dünner ... Ohne Zweifel hat er auch eine Elasticität, durch die er sich bemüht, sich nach allen Seiten auszubreiten, und in die Räume zu bringen, die leer sein könnten ... Ich zweifle selbst nicht, daß die Zusammendrückung der Luft im Schießpulver ein Wert von der Gewalt der Elasticität des Aethers sei; und weil wir aus der Erfahrung wissen, daß die Luft darinn beinah 1000 mal dichter ist als gewöhnlich, und daß in diesem Zustande ihre Elasticität eben so viel mal größer ist, so müßte die Elasticität des Aethers eben so groß, und also 1000 mal größer sein, als die gewöhnliche der Luft ist. Wir werden uns also einen richtigen Begriff von Aether machen, wenn wir ihn als eine der Luft ähnliche flüssige Materie ansehen, nur mit dem Unterschiede, daß der Aether ohne Vergleich feiner, und also auch weit elastischer ist als die Luft."1

The views presented in this popular scientific work are basically the same as in the more serious scientific treaty "Nova theoria lucis et colorum", 1746-51,1, III. Euler 1986. 23. Letter 19.

194 [...]Was die Fortpflanzung des Lichts durch den Aether betrifft, so geschieht sie auf eine ähnliche Art mit der Fortpflanzung des Schalls durch die Luft; und so wie eine in den Theilen der Luft hervorgebrachte Erschütterung den Schall wirft, so macht eine Erschütterung in den kleinsten Theilen des Aethers das Licht oder die Lichtstrahlen aus ... Das erste, was uns hierbei vorkommt, ist die erstaunliche Geschwindigkeit der Lichtstrahlen ... In unserem System ... ist sie eine notwendige Folge unsrer Grundsätze ... Diese Grundsätze sind die nämlichen mit denen, worauf die Fortpflanzung des Schalls durch die Luft herrührt. Es hieng diese Fortpflanzung theils von der Dichtigkeit der Luft theils von ihrer Elasticität ab ... Wir wollen uns vorstellen, die Dichtigkeit der Luft würde so sehr verringert, und ihre Elasticität so sehr vermehrt, daß die der Dichtigkeit und der Elasticität des Aethers gleich wäre; so würden wir uns alsdann nicht mehr wundern, daß die Geschwindigkeit des Schalls mehrere tausendmal größer würde, als sie jetzt ist.5'2 [.. .]Nun muß man sich in allen Theilen der Sonne eine beständige Bewegung vorstellen, durch die sich jedes Theilchen sich in einer immerwährenden Erschütterung und Schwingung befindet. Diese theilt sich dem angegrenzten Aether mit, und erregt darinnen eine ähnliches Zittern, daß hernach immer weiter und weiter nach allen Gegenden ... fortgepflanzt wird ... Aber das ist sehr natürlich, daß die Schwingungen, die das Licht hervorbringen, weit lebhafter und schneller sein müssen als die, aus denen der Schall entsteht; weil der Aether ohne Vergleich feiner ist als die Luft. Da eine schwache Bewegung nicht im Stande ist, die Luft so weit zu erschüttern, um einen Ton hervor zu bringen; so sind auf gleiche Art die Bewegungen einer Glocke und der übrigen schallenden Körper für den Aether zu schwach, die Erschütterung zu bewirken, die das Licht ausmacht ... 3000 Schwingungen in einer Sekunde sind für den Aether zu viel zu grob und zu langsam. Es gehören weit öftere Schwingungen ... dazu, wenn sie im Stande sein sollen auf den Aether zu wirken, um eine Erschütterung in ihm hervorzubringen."3 [...]Woher kommt es, daß die bloße Erleuchtung im Stande ist, aus [den] bunten Körpern Stralen hervor zu bringen?1*4 [...]Die leuchtenden Körper müssen mit musikalischen Instrumenten verglichen werden, die ... einen Ton geben ... die dunklen Körper hingegen ... müssen ... mit gespannten Seiten verglichen werden, die in Ruhe sind ... Betrachte Ihre Höhheit nur einmal ein Ciavier, worauf nicht gespielt wird, zu der Zeit, wenn auf einer Geige der Ton ... angegeben wird. Sie werden sehen, die Seite von eben diesem Ton wird anfangen zu zittern, und sogar ihren Ton hören zu lassen, ohne berührt zu sein ... dieselbe Erscheinung kann also bei den dunklen Körpern statt haben, und diese können auch durch die bloße Beleuchtung in Bewegung gesetzt werden."5 Below is the list of physical similarities between air and aether extracted form the above passage, comprising those resulting from their both belonging to the category "fluid" (above the dotted line) and other, optional properties of fluids (under the dotted line). AIR

air vibrations are sound strings, bells

392 M! 394 MS

ibid.: 24. Letter 20. ibid.: 26. Letter 21. ibid.: 27. Letter 23. ibid.: 30-31. Letter 26.

FLUID corpuscular structure density elasticity carrier of vibrations incited to vibrations by oscillatory motions of solid bodies

AETHER

aether vibrations are light shining bodies, the sun

195 invisible light to imponderable low density its vibrations produce sensory effects3" acoustic resonance

resonance effects

radiation of dark bodies

We see that the similarity between the subjects of comparison, sound and light, was assumed to be literal due to the physical objects involved - air and aether, respectively - sharing essential physical properties. 7.2.2. The abandonment of the aether theory For a century, the theory of light as waves in aether, supported, among others, by Huygens and later Euler and Bernoulli, found a superior rival in the corpuscular theory. A major difficulty which the theory encountered was the polarisation of light beams on the Iceland crystal, which could only be satisfactorily accounted for in terms of corpuscular theory. The difficulty lay in the fact that, in view of the supposed physical similarity of aether and air, in the wave theory only the possibility of longitudinal waves was seriously considered. It was assumed that all undulations are propagated through homogenous mediums in concentric spherical surfaces like the undulation of sound, consisting in the direct and retrograde motions of the particles in the direction of the radius, with their concomitant condensations and rarefactions. The discovery by Young that light shows diffraction and interference strongly supported the wave theory (and, at the same time, it centralised the position of these effects in the notion of wave itself). In the beginning of the 19th century Fresnel and Young modified the theory with the assumption that the waves are transversal. Young compared light to the undulations of a cord agitated at one of its extremities, and Fresnel pointed out that a body is capable of transverse vibrations if we suppose it possesses rigidity, or the power to resist distortion. This meant, however, that aether could no longer be regarded as similar to air as a kind of an elastic fluid because only solids are capable of propagating transversal waves. The nineteenth century was marked by multiple attempts to develop a mechanical model of the aether which would "save the phenomena", that is, to "invent" a substance which would offer no resistance to the movement of the celestial bodies and, at the same time, the particles of which would be capable of displacement propagating itself by means of a transversal wave and compatible with the laws of light propagation,397 but none of them actually succeeded.

The affinities concerning this point extend beyond the bare fact of producing some kind of non-tactile sensation; similarities of perceptual effects are reflected in language in such synesthetic metaphors as sharp sound and sharp light, a sound striking a person's ears just like light strikes a person's eyes, or forceful sound and forceful light, and in the notion of harmony applicable to both of them. E. g. by Fresnel, MacCullagh, and Cauchy.

196 The works of James Clark Maxwell, based on the concept introduced earlier by Faraday and given a mathematical interpretation by Thomson of the "fields" of electric and magnetic energy, followed by the electromagnetic theory of light in 1863, initiated a new trend which was eventually to eliminate the question of the mechanism of light propagation in terms of the mechanical properties of the aether. It changed the direction of the research, establishing its programme as a search for energies in the aether, based on the idea of a conserved physical quantity converted from one form to another in the operations of nature. Mechanical models proved irrelevant to the description of phenomena as soon as they were formulated in terms of changing distribution of energy. Whereas some physicists still insisted that the ultimate goal should be the adequate mechanical model of aether, others sought more general mathematical structures, whose validity did not depend on a mechanical representation of them. In the late 19th century, "the aether ... increasingly took on the role of a mere symbol for the electromagnetic field, rather than a mechanical structure".398 In 1890, Hertz reformulated Maxwellian equations for free aether providing a picture of a pure electromagnetic field, independent of any mechanical considerations. Dessauer (1958: 58) commented on the concept of aether saying that ... der ,Aether' ist nie etwas gewesen als ein Postulat, ein Verlangen unseres beschränkten Verstandes nach Anschaulichkeit, nach Stütze aus dem Bereiche des schon bekannten, nach etwas, was man ,denken' im Sinne von ,sich vorstellen' könne, nach einem Modell. Das Zeitwort ,schwingen' suchte nach einem Subjekt, hat einmal ein großer Physiker gesagt. ,Aether' füllt nur scheinbar den syntaktischen und gedanklichen Ort.

The abandonment of the aether hypothesis, completed in 1887 through Michelson and Moreley's experiment which demonstrated the non-provability of the aether, and its replacement with the concept of a non-material field of force, accompanied by the mathematical redefinition of wave eliminating the need for its mechanical interpretation, amounted to generalisation of the wave concept so that the relatively central component of its meaning - propagation by the displacement of particles of, or stress in, a material medium - turned into a marginal optional component. According to our account, the notion of "wave" came to be applied in an extended sense, that is, metaphorically, to the same range of phenomena where it had formerly been applied in a literal sense. The metaphor is "dead" immediately: generalisation of meaning and its lexicalisation are two coexistent aspects of the same linguistic event. We assume that the survival of the notion of wave, or "undulation", through meaning generalisation after the elimination of the mechanical hypothesis was possible owing to the ubiquitous metaphor "change=movement". The same process of generalisation of meaning through generalisation from spatial displacement to other kinds of change took place in case of other words related to the concept of undulation, verbs which originally denoted a periodic change of position of a material particle and came to denote periodic change of other parameters: oscillate, vibrate, fluctuate, and nouns derived from these verbs: oscillation, vibration, fluctuation, see page 134.

Wise 1990, 342-356: 353.

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7.2.3. Further development Further generalisation of the notion of wave came with wave mechanics; the waves it describes are waves in multi-dimensional space, and are not directly measurable. Apart from sharing the same mathematical formalism with the other kinds of waves, they also show the interference, diffraction, and superposition. The probabilistic interpretation of Schrödinger's equation as referring to the probability of localisation of a particle amounted to an even more profound change in the structure of the concept "wave" than the earlier reconceptualisation of light wave as propagation of immaterial "field of force", and deBroglie's matter waves. "Wave of probability" is not even propagation of a series of continuous changes of physical measurables. The concept of the wave of probability does not imply that there is something physical spreading out according to the wave function; rather, it is similar to the explicitly metaphorical notion of "crime wave". The following quotation from Hütten (1958: 164) summarises aptly the history of the concepts of aether and wave: The concept of wave originally stems from observations of elastic waves, the waves we can produce in water, or on a string. It is a mechanical model, and the waves require a medium to carry them. When wave theory was applied to light, an aether was postulated for this purpose. But this mechanical interpretation is too limited for explaining optical phenomena, though the elastic theory of light can be made to work to some extent. Our increasing knowledge of optics thus made it necessary to re-interpret the concept of wave. In mechanics, 'wave' is interpreted by the picture of a medium in motion; the geometrical shape of the medium, and the displacement of its particles, is taken as the main property designating the term 'wave'. In Maxwell's theory the particle picture is suppressed, and instead of the displacement of particles from some equilibrium position we have the concept of energy to characterise the processes. The field interpretation of electromagnetic theory still allowed us, however, to make use of a continuous medium, though we had to strip the medium of all its mechanical properties. Thus the aether became a very tenuous thing: it had no weight, it could penetrate all bodies - in short, it acquired a ghost-like character. Relativity taught us to give up the concept of aether altogether, and we became accustomed to regard electro-magnetic waves as energy held together in a wave-pattern which could travel even in empty space. Finally, the socalled matter waves in quantum mechanics turn out to be still more 'abstract'; and all that remains of the original wave model is a statistical distribution.

7.3. Life stories of metaphor: from metaphorical to literal and literal to metaphorical In section 3.1.2.1., we claimed that Turbayne's account of the life story of metaphor as starting from a stipulation of meaning and undergoing a gradual transition to the status of a literal description does not fully account for all kinds of metaphorical processes. Below we contrast Huygen's notion of sound wave as an example of a metaphorical process leading to meaning change in accordance with Turbayne's description - a stipulative metaphor - with two examples of assimilative metaphors which started their existence as literal descriptions. We identify stages of development within the metaphorical process, different for both kinds, which we define in general terms (STAGE), and indicate what in particular happened to the concepts involved at each stage (PROCESS).

198 CONCEPT

STAGE

PROCESS

Case A: from metaphorical to literal (Turbayne's account) wave as applied to sound: Huygens(1690)

production: highlighting an analogy

circular wave-front two-dimensional in water waves conceived as analogical to spherical wave-front in threedimensional sound propagation

establishment: merging of two fields of meaning propagation of a disturbance in a material medium through oscillation of its particles becomes the defining property of the wave concept death: generalisation of meaning completed Case B: from literal to metaphorical light wave: e.g. Euler (1769)

production: an application of a concept to a new instance on the basis of the identified shared features of the concept and the instance

light conceived as a propagation of vibrations in the material medium (ether) of known physical properties (density, grained structure)

detachment: disanalogy discovered, the need of correction of hypothesis acknowledged; the field of meaning falls apart into two partially overlapping fields of meaning

recognition of difficulties with assigning physical properties to ether, emergence of the field concept

death: generalisation of meaning through re-structuring of the conceptcore/margin shifts

interference, reflection, refraction, and the applicability of the wave equation independent of the existence of a

199 material medium become defining properties of the wave concept el. current of the fluid theory of electricity

production: an application of a concept to a new instance on the basis of the identified shared features of the concept and the instance

propagation in conductors, electric wind, Leyden jar experiments, etc. observed and classified as an instance of storage and movement of fluid matter

detachment: disanalogy discovered, the need of correcting the hypothesis acknowledged; the field of meaning falls apart into two partially overlapping fields of meaning

recognition of ponderability as a defining property of a substance, emergence of the field theory

death: stabilisation of two different senses of an expression

"electric current", "electric density" etc. preserved as set phrases after the abandonment of the fluid theory

The examples above illustrate the two alternative ways for the establishment or re-establishment of a metaphorical meaning of an expression as literal: • the establishment of a new distinct, albeit conceptually related meaning; the word signifying a concept is typically complemented by another word ("electric current") with which it constitutes one terminological item (term) which is not paraphrasable with usual linguistic (syntactic) means, even if it used to be so in the "literal" stage ("current of electricity"). We call such expressions satellite metaphors of an extended (conceptual) metaphor juxtaposing, in our example, hydraulic and electrical processes; • restructuring of a concept by means of core/margin shifts in the semantic field (the existence of a medium became non-essential for the concept of a wave). In exact sciences it is accompanied by a formal re-definition of a concept in the specialist language, based on new recognitions in the domain under study. Both processes apply to assimilative metaphors as well as to the conventionalisation of metaphorical expressions of a stipulative kind.

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8. Theory-constitutive and educational metaphors We initially outlined the distinction found in literature on the subject between theory-constitutive and exegetical metaphor, defining the former as constituted by non-paraphrasability and its role as a guide in further research. In what follows we illustrate the difference between theory constitutive-metaphor, "deep" educational metaphor helping a learner to grasp theoretical concepts, and superficial, decorative extended metaphors of the kind which has become commonplace in popular scientific writing. Both theory-constitutive and educational metaphor perform the function of explaining the recipient subject, making it understandable in terms of the donor subject. The difference is that in the former case, the theory explaining the recipient subject offers no other understanding of it above and beyond this conceptualisation; the recipient subject has no understandable, structured representation outside the metaphorical model, so it is not distinguishable within the theory from the model. In an educational metaphor, the recipient subject makes sense independently from the donor subject; the differences between the thing modelled and the model are acknowledged and can be pointed out. They should be pointed out to prevent identification of the things modelled and the metaphorical representation, because these differences constitute surplus knowledge of the recipient subject compared to the representation via metaphor. A metaphorical representation always gives only a partial understanding, but in a theory-constitutive metaphor the part stands for the whole - nobody understands more of it than is made possible by means of this representation. In the case of an explanatory metaphor, the educator is in possession of the surplus knowledge; the learner initially lacks it and can be misguided by the metaphor if taking it for the whole. Not every educational metaphor is associated with that kind of danger. In some educational metaphors, the learners themselves can easily identify the relevant differences between the donor and the recipient subject. It has become customary for the popularisers of science re-formulating the results of contemporary research for presentation to non-experts to use extended metaphors; many of them are merely decorative rather than a key to understanding. The easier it is for the learner to identify disanalogy without further instruction, the more superficial the metaphor, the less cognitive gain it brings, the less we can talk of understanding the recipient subject being reached via the donor. In a way, it seems that an effective educational metaphor is a "dangerous" one (capable of being misunderstood).

8.1. Constitutive metaphor: waves of probability The concept of probabilities propagated in waves illustrates the function which a metaphorical model may play in scientific explanation. In an effect known as quantummechanical tunnelling, uncertainty of position of a particle described in Heisenberg's principle allows the particle to vanish on one side of an energy barrier and reappear on the other side. In two-photon experiments, a puzzling result has been observed: of two photons sent out from a source, the one which tunnelled through a barrier before reaching the detector arrived sooner than the one travelling freely to the detector, which means that the former travelled with superluminal velocity - impossible according to relativity. "Waves of probability" provide a satisfactory interpretation of "rapid tunnelling". In a current interpretation of

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matter-particle dualism, a moving elementary particle is represented as a wave packet, rising to a certain height and sloping down. The height of the wave at a given position along this span indicates the probability that the particle occupies this position: the higher a given part of the wave packet, the more likely it is that the particle is located there. The length of the tunnelling wave packet is interpreted as corresponding to the probability of occurrence of the associated event. At a barrier, the wave packet representing the probability of location of a photon is split into a larger part which is reflected - because reflection is more probable than tunnelling - and a smaller (shorter) part which tunnels through the barrier. The wave packet becomes reshaped during its journey: it is shortened, so that its peak comes closer to the front. The peak represents the most probable location of the particle, and the one at which it is detected by the target detector; in this way, it is detected sooner than the other particle, associated with a longer wave packet. The detection of a particle at a definite location is said to destroy the corresponding wave packet. This is a theory-constitutive metaphor because there is no explanation for the involved phenomena besides the explanation applying the concept of probability distributions as wave packets. The experiment being modelled in terms of probabilities spreading in waves allows us to conceive probabilities as "sort-of" things, capable of being split, propagated, reflected, reshaped, and destroyed. In turn, the interpretation of wave packets as carriers of probabilities rather than something physical allows us to accept the paradox of its spreading with superluminal velocity as not violating Einstein's dictum. Thus, a sense of cognitive satisfaction is attained: the results of the experiment can be assimilated into the existing framework of knowledge. The metaphor allows us to use concepts born of ordinary experience to reason about areas which lie beyond possible experience. The cognitive satisfaction it gives, however, is nothing like the "objective knowledge" of earlier periods of natural science; we referred to this complex of issues when discussing contemporary physicists' self-reflection, indicating how theory-constitutive metaphors of modern physics pose as many questions as they appear to answer.

8.2. Educational metaphor: curvature of space Educational metaphors are invented, or taken over from earlier phases of a theory, to help students grasp a physical idea of which the expert possesses a representation independent of the metaphor. They familiarize physical concepts to students, making them similar to concepts known from ordinary experience, but it is possible, and often necessary, to explicitly point out the disanalogy between the recipient and the donor subject in order to prevent the analogy being overstated. The expert is able to identify the distinctions between the complete representation of the recipient subject, containing all knowledge of it available at a given stage, and the partial representation by analogy with the donor subject. Examples are educational metaphors based on, and advancing, the linguistic metaphor "curvature of space", motivated by mathematical analogy (see page 201). It incites the application of concepts associated with the donor subject (shapes in three-dimensional space) to explicate concepts within the recipient domain (space-time). The authors exposing the spacetime concept in non-mathematical language face the task of explaining how space-time curvature produces the effects observable in three-dimensional space, such as a curved path and the acceleration of a moving object. This means a conceptual transition from four-dimensio-

202 nal space-time to three-dimensional "normal" space. The image of a surface curved in three dimensions as a representation of the space-time curvature, imposing itself through the identity of denotation, is frequently applied in education to make relativity conceptually available to students. As an example of such a pedagogical application of the "curvature" analogy, consider a demonstration proposed by Ehrlich (1990: 13) in the section on "Gravity and Curved SpaceTime" in his collection of physical demonstrations intended for the secondary school level: The curved time-space interpretation of gravity in relativity theory can be simulated by rolling balls on a stretched transparent membrane placed on an overhead projector ... According to general relativity, gravity is not due to a force, but rather to the curvature of space-time caused by the presence of matter, and that curvature or distortion affects how other matter moves. The demonstrator is instructed to roll gun bullets across the surface of a stretched membrane. If another steel ball is placed at the centre of the membrane, causing it to be appreciably distorted, the bullets rolled from the edge of the membrane will "go into orbit" about the centre ball if their speed is low enough, or else be deflected by the curvature of the membrane and strike the hoop on which it is stretched. The formation of stars, planets, or galaxies due to mutual gravitational attraction of many separate particles for one another can be simulated using some number of BB's placed at random points around the membrane; the membrane having been shaken, soon all the BB's coalesce.3" This example shows how an attempt to visualise the metaphor of space curvature may be conceptually misleading, encouraging misconceptions depending on the associations connected with the term "curvature" and "curved" in their usual meaning. The demonstration may be interpreted as conveying the wrong idea that the effect of space-time curvature manifests itself merely in the change of a shape of the path of an object in space, deemphasising acceleration as an effect of the non- Euclidean character of space-time. It makes it easy to forget that, in the three-dimensional representation of space-time, a curved line represents the path of an accelerated object. The conceptual transition from four-dimensional space-time to three-dimensional "normal" space is sometimes achieved by educators by means of a sailing ship analogy, involving the transition from two-dimensional to three-dimensional consideration of the path of a moving object: In relativity ... both matter and space are fused into a single non-Euclidean continuum, with curvature varying from place to place and from one moment to another. Gravitation and accelerated motion are no longer interpreted as the results of forces acting in space, but follow naturally from the curvature of the four-dimensional continuum . . . Just as a ship moving across the ocean moves along a curved path in virtue of the curvature of the earth's surface, a physical body contained in a local curvature of time-space moves in accelerated motion.400 The limitations of the sailing ship analogy lie in the fact that the spherical sea surface is a completed entirety on which a ship moves along a certain pre-existing track; a body moving in Euclidean three-dimensional space of classical physics occupies successively different positions. It is by analogy to this space that we tend to speak of a body "moving" in a nonEuclidean space-time. But the correct interpretation of relativity is such a fusion of space and Ehrlich 1990: 17. Capekl961: 146.

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time in which they cannot be separated. The space curvature of the relativistic theory of gravitation varies with time. Therefore, it is incorrect to conceive of the pre-existing nonEuclidean structure of space, constraining bodies to move in certain ways like a pre-existent system of channels constrains them to run on certain paths (cf. Capek 1961: 146). The error lies in assuming a pre-existent path in space which is there before and after motion along which the material object moves, and along which other material objects may move in a later time; a later moving point cannot pursue the "same" course, since its time-co-ordinate is different, which means that its space-co-ordinates are also different. 8.3. From explanation to rhetoric In popular writings for informally introducing physical theories to non-experts, a newly invented metaphor has become a favourite means of expression and is used sometimes for its own sake, i.e. as an aesthetic rather than explanatory means. An example is a popular scientific exposition of "rapid tunnelling" outlined above (cf. page 201-202). In this text, the effect, explained - in the theory-constitutive sense of the word "explain" - using metaphorical concept of waves of probability, is presented to the non-expert by recourse to another metaphor of a very different kind. The position of a photon on its way from the source to the detector being described by probability distribution, the bell-shaped graphic representation of this distribution motivates its being compared to a tortoise shell. Extension of the comparison follows in the fragment explaining the difference of the arrival times of the tunnelling and the freely travelling photon: A relapse into metaphor might help to explain the point. The nose of each tortoise leaves the starting gate the instant of opening. The emergence of the nose marks the earliest time at which there is any possibility for observing the photon ... But because of the uncertainty of the signal's location, on average a short delay exists before the photon crosses the gate. Most of the tortoise (where the photon is more likely to be detected) trails behind its nose ... When tortoise 2 reaches the tunnel barrier, it splits into two smaller tortoises: one that is reflected back toward the start and one that crossed the barrier ... We observe that the peak of tortoise 2's shell, representing the most likely position of the tunnelling photon, reaches the finish line before the peak of tortoise 1's shell ...'*"

In this fragment, "tortoise" stands for "wave packet", "nose" stands for "leading edge", "finish line" stands for "detector", and "peak of the tortoise's shell" stands for "peak of the wave packet". The difference this replacement makes pertains to aesthetics rather than to understanding or ease of expression. The usual function of metaphor as means of cognition and expression is to provide conceptual, semantic and syntactic rules for the linguistic handling of the subject under consideration by recourse to the donor subject. The tortoise as the donor subject provides no rules beyond those which are already contained in the concept of wave packet because a tortoise being split or reflected at a barrier violates semantic rules governing the application of the word "tortoise". What happens is the contrary of the usual explanatory application of a concept, and to the authors' proclamation at the outset of the fragment quoted: whereas in the usual explanatory metaphor the explanandum (the thing to be explained) borrows the structure from the explanans (i.e. light borrows structure from a tennis ball and is thrown and reflected from a mirror), here it is the apparent explanans - the tortoise - which receives the properties of the wave packet. What remains of metaphor is a 401

ScAm, Aug. 1993:40.

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mere substitution of words. This example proves the high status which metaphor has attained as educational means in popular scientific writing on physics, its application becoming customary to such an extent that it has emancipated itself from the initial, explanatory purpose, and is used excessively if judged with respect to this purpose. Metaphors of this kind are a matter of style and rhetoric rather than a matter of conceptual support in the acquisition of concepts. (See, however, page 211.)

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9. Metaphor and style: "figures of speech" in the language of physics ?.l. The position of "figures of speech" in the discourse of physics Consider the following statements: Any electron around would thus be welcome to help out, or the impurity nucleus might actually consider stealing an electron from the next site,402 Other parts of the wave became noisier.403 In such regions we lose time's arrow ... When the random element has reached its limit and become steady the arrow does not know which way to point.404 Another possibility of avoiding the heat death is by killing the universe in a different way.405 If the gas and the light are in equilibrium, it can be shown ... that Maxwell's demon will be as blind as if there were no light at all.406 (emphasis HP) In the italicised parts of the first utterance, the means of expressions are drawn from the personification of electrons and atomic nuclei. The second utterance is based on the metaphorical notion of "noise", generalising the meaning of the word applied primarily to acoustical phenomena to (usually unwanted) random fluctuations of any kind of signal. Whereas "noise" in this generalised meaning is an item of terminology, the adjective "noisy" applied to a signal showing such fluctuations does not belong to terminology, but is immediately understandable to the reader knowing the two meanings of "noise" and the usual meaning of the adjective: it belongs to elementary linguistic competence to be able to generalise the meaning of the adjective on the basis of the generalised meaning of the noun. The following three utterances are based on figures of speech coined at some point of the development of thermodynamics and continuing their existence as lexicalised items - "arrow of time", "heat death", "Maxwell's demon": • "Death" in "heat death" (the future thermal equilibrium of the universe anticipated by the second law of thermodynamics) carries with it the notion of killing as a part of its semantic field, or meaning component, and lets the verb "kill" be applied to the universe. • "Maxwell's demon" has been called a valve by its originator, and contemporary expositions of the Gedankenexperiment constituting the frame of its existence point out that it is to be conceived of as a device rather than a creature; still, the personified denotation of the device makes it natural to apply to it the personified mode of speaking, e.g. the property "blind" literally predicated of animate creatures. • "The arrow of time", as we argued before, is developed upon the spatial conceptualisation of the present as a point moving on a line by means of an ontological metaphor making this point to an asymmetrical object - an arrow. In the utterance above, the metaphorical mode is pushed even further- the recipient subject of this spatial-ontological metaphor is personified, made compatible with the verb "know", requiring, in the literal mode of speaking, that the subject of the predicate be an animate creature. 402 405 404 405 406

Solymar and Walsh 1970: 141. ScAm, May 1988:32. Eddington 1928: 78. Kubatetal. 1975:24. Wiener 1954: 30.

206 All the emphasised expressions above are similar in one characteristic: they are metaphorical in a way which is a matter of style rather than a hardly dispensable means of conceptualisation essential for our ability to mentally "do things" with our objects of reflection. They could relatively easily be paraphrased in more abstract wording avoiding metaphorical mode. While richer in associations or more concrete and visualisable, they are of little consequence for the shape of models and theories involving the concepts they are deployed in exposing. Physical theory (as well as methodology and terminology) could do without them without making any difference to itself.407 They remind one of the notion of a "figure of speech", which was what metaphor was essentially held to be before Richards' pioneering insights in this century. Probably the most important motivation behind the use of this metaphorical mode, not only in popularising science and philosophical reflection, but also in handbooks and in scientific texts,408 is that it allows a more compact, linguistically simpler formulation of complex ideas than could be achieved in literal formulations applying more abstract terms, but other factors contribute their own impulses as well. Most generally, the stylistic impact of such metaphorical expressions is that they make the language of the expositions of physical ideas in which they appear more like non-scientific varieties of language: the language of literature and everyday speech. The style of specialist texts on physics is distinguished by a number of characteristics belonging to the fields of syntax, lexicon, and text grammar. The application of metaphorical figures of speech reduces these differences because metaphorical mode is frequently used in non-scientific language varieties, and because they enhance such aspects of the texts as concreteness and imaginability, as well as relatedness to other domains of experience. One problem with the impact of the specialist languages of science upon the reader is that their special characteristics - the abstractness due to the extensive use of defined theoretical terms, the high average length of nominal phrases, etc. - stress the high intellectual demand on the reader and may have a discouraging effect. Metaphorical speech of the kind presented in the examples above paraphrases what could be expressed in more abstract terms; and for an average learner or "on-looker", de-abstracting physical concepts makes them less discouraging. The other above-mentioned difference which the metaphorical stylistic devices make compared to non-metaphorical wording is the relatedness to other domains of experience and discourse. The "figures of speech" invented for the presentation of physical ideas make an 407

408

This applies without reservations to the coinages "heat death" and "time arrow". With Maxwell's demon the situation might be more complex because there have been physics experts whose statements can be interpreted as making a point of the "demon" being an animated being, and it is possible that the verbal personification of the concept (in its original exposition and in the denotation) facilitated to some extent the coming into existence of the association between thermodynamics and information theory (relating entropy and information). The latter would mean that the metaphor of "demon" has been not merely a matter of wording but a relevant factor in the conceptual growth of the physical theory, if not at its core then at least at its outskirts: at the interface between physics and information processing. Anyway, the influence of this metaphor upon physical theory and concept formation is obviously weaker than for example the role played in them by the notion of force, where anthropomorphism gave origin to a basic physical concept, or by spatialised models of energy, where physical concepts are rendered by means of deeply rooted, ubiquitous spatial metaphors as elements of structures (models) which can be conveniently processed visually and, therefore, conceptually. Examples of the use of "arrow of time" in expert communication are to be found in:Andretsch and deSabbata 1990: 318, 350, 382, 393. "Heat death" appears, for example, in Davies 1977: 189, 192.

207 impact upon the imagination of the reader and strongly trigger the appropriation of physical ideas in other branches, evoking extra-scientific associations and suggesting their direct human relevance. Even if not exactly the same is meant, "the arrow of time" belongs to the language of Shakespeare as well as of Eddington, and the two discourses - literature centred upon human beings on the one hand, and science centred upon nature on the other - appear to be closer to each other. It is very doubtful whether "Maxwell's valve" would have found its way into literature and literary criticism, as Maxwell's demon has. Thermodynamics, with its 2nd law of thermodynamics, Maxwell's demon, heat death, and time's arrow is the most interdisciplinary of all branches or theories of physics, evoking most direct associations with the human sphere, from its origins in the 19th century till the present day. Its philosophical, psychological, human relevance is reflected in its language, offering metaphorical, picturesque reformulations of what can otherwise be stated in a more mundane mode. We could speak of "thermal equilibrium" of the universe rather than of its "heat death", "irreversibility of physical processes" rather than "the arrow of time". These coinages, however, make science sound more like poetry and drama, and this is consistent with the extra-physical dimensions of the second law, which have, more than any other law of physics, encouraged the reflection on its consequences in other dimensions of human existence: psychology, art, history, economy, and sociology. Making the language expressing the insights of physics more like the language of other genres of creative writing, the picturesque metaphors of thermodynamics also encourage the implementation of its ideas in literature. In what follows we present briefly the three metaphorical "figures of speech" associated with the second law of thermodynamics as exemplifications of what we refer to as a stylistic or rhetorical dimension of metaphor in the language of physics. They originated in educational metaphors which have gained popularity and have been lexicalised through repeated use.

9.2. The arrow of time The phrase "arrow of time" was coined by Eddington in 1928 (cf. Eddington 1964: 76) and has functioned ever since as a shorthand for a complex of assumptions made about the nature of the physical world connected with the existence in nature of irreversible processes, i.e. processes taking place in systems whose initial states cannot be restored through a chain of changes governed by the same laws of nature which led to the elimination of these initial states. Irreversible processes cannot "run backwards": they are asymmetrical. To illustrate the point, the irreversible processes are usually contrasted with the processes governed by the laws of classical mechanics, where the reverse of every equation describes a possible process of nature. The words "irreversible", "reversible", "asymmetrical", "forward", "backwards" applied to processes are themselves cases of spatial metaphor involving the metaphorical conceptualisation of states of a system (ranges of values of parameters) as positions in space, which is equivalent to the conceptualisation of change as movement. Movement is the change of position of a physical object in space. The "going on" of processes means successive change of the state of a physical system (i.e. one or more physical quantities characterising this system). The notions of "reversibility" and "going backwards" of physical processes turn successive states of a system into positions on a line. In these expressions, the transition of

208 a system to a state identical with an earlier state becomes conceptualised as a return to an earlier position. The ground for the transfer of meaning in the metaphor "time's arrow" comprises two aspects. The first of them is the customary conceptual and linguistic representation of change as movement. "Arrow of time" is a conceptual and linguistic development of the concept of time as a moving object - dissociated, however, from the concept of absolute time in favour of identifying "time" with processes of nature. From the two versions of the metaphor rendering time as an object in relative movement with respect to the observer (cf. section 4.1.2.4), it incorporates the version where the ever-changing present of the processes of nature is represented as a movement of an object in space forward in a straight line. In addition to this, the metaphor utilises an arrow's property of directionality, i.e. the nonidentity of its two ends, to express the complex of meaning attached to the question of an absolute difference between past and future. The fact that by its being differentiated in space an arrow could become a carrier of time-related connotations is conceptually consistent with notions such as direction, directionality, irreversibility, reversibility, symmetry, and asymmetry being used with reference to both the relation of juxtaposition in space and the relation of succession in time. In each of its particular applications, the expression "time's arrow" may refer to one or more of the three factors characterising the aforementioned difference: • the continuous increase in any closed system - as well as in the cosmos as a whole - of the parameter known as entropy (inverse of the statistical probability of the occurrence of a given state of a system), described in the second law of thermodynamics ("the thermodynamical arrow of time"). The metaphor of an arrow points to the difference between the initial and a later state of a closed system, lying in the fact that there is no way leading from the later state to a state identical with the initial one; • the continuous expansion rather than the contraction of the universe ("the cosmological arrow"); • the psychological factor concerning the subjective experience of time passing and the difference between past and future events: the impossibility of remembering the future ("the psychological arrow"). The phrase "arrow of time" belongs to a species of metaphors which introduces picturesque elements to the vocabulary of physics without contributing through their usual connotations any particular metaphysical, ontological, or epistemological assumptions of their own. It is a "figure of speech" which reduces a complex aggregate of independently formulable theoretical assumptions to a compact expression which is linguistically easily manipulable, illustrated by formulations like: In such a region we lose time's arrow. You remember that the arrow points in the direction of increase of the random element... When the random element has reached its limit and become steady the arrow does not know which way to point.409

Eddington 1928, 1964: 78.

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What is meant is that after a system has reached a state of greatest probability (maximum of entropy), the results of measurements taken at two different times cannot indicate which of them had been taken earlier. The more perfect an instrument is as a measurer of time, the more completely does it conceal the time's arrow.410 What is meant is that our clocks depend in their functioning on cyclical processes in which the dissipation of energy leading to the increase of entropy is eliminated as far as possible. There must be well-defined thermodynamic and cosmological arrows of time, but they will not point in the same direction for the whole history of the universe.4" What is meant is that the expansion of the universe and the rise of entropy are independent processes.

9.3. Heat death The phrase "heat death" was coined by J. Jeans in 1930 in the context of the implications of the second law of thermodynamics for the future of the universe. It denotes its final state of thermal equilibrium anticipated by the second law. The forerunner of the concept so denoted in the history of "futurologist cosmology" is the Stoic concept of εκπυρωσις, the destruction of the world by fire at the end of each particular world-cycle. What they share is the idea of the universe ending in disintegration; the difference lies in the way in which the destruction is completed - by the violence of fire in one case, motionlessness in the other. (Jeans may have been aware of the similarily between these two concepts and acquainted with the Stoic conception of the world as a living organism, in which case one might speculate that these two factors together faciliated the coinage of his animist metaphor. As we will see in what follows, however, this conjecture finds little support in the "close reading" of Jeans' text.) The similarity between a dead creature and the universe in thermal equilibrium which sufficiently justifies the transfer is the cessation of motion and processes which took place before.412 In fact, however, the motivation for Jeans' metaphorical application of "death", "dying" extended beyond this common aspect. It included the causal relationship between the "thermal death" of the universe and the consequent extinction of life on the earth (and other planets). This constitutes the context for the original use of the words "death" and "dead" with reference to the cosmos: It is the tragedy of our race that it is probably destined to die of cold ... The sun ... must necessarily emit ever less and less its life-giving radiation ... This prospective fate is not peculiar to our earth; other suns must die as our own, and any life there may be on other planets must meet the same inglorious end. Physics tells the same story as astronomy ... the second law of thermodynamics predicts that there 410 411 412

ibid.: 99. Hawking 1988: 145. Today, "heat death" does not mean the absolute absence of any changes: in the state of thermal equilibrium, certain local fluctuations of thermodynamical potential may still take place, but macroscopic processes are absent.

210 can be but one end to the universe - a 'heat death' in which the total energy of the universe is uniformly distributed, and all the substance of the universe is at the same temperature. This temperature will be so low as to make life impossible. It matters little by what particular road this final state is reached; all roads lead to Rome, and the end of the journey cannot be other than universal death.413 He continues in the same picturesque, literary style, constituting the context and the origin of the phrase "heat death": Entropy cannot stand still until it has increased so far that it can increase no further. When this stage is reached, further progress will be impossible, and the universe will be dead. Thus... nature permits herself, quite literally, only two alternatives, progress and death: the only standing still she permits is in the stillness of the grave.414 In Jeans' text we observe the shift of reference of "heat death" from the effect - the extinction of life on the earth - to the cause: increasing thermodynamic homogeneity of the universe ("dying" of the universe) up to the maximal possible ("dead") level.

The expression "heat death" has been used subsequently by other authors to refer to thermodynamic future of the universe without any reference to destruction of life on the earth, so that the latter connotation has been marginalised (of course, the causal relationship is acknowledged and can be recollected when needed), and today the phrase owes its comprehensibility to the apprehension of similarity between an animal and the cosmos in their respective "dead" states. Thus, the phrase "heat death" (later also "thermal death" and "cosmic death") can be regarded as a linguistic manifestation of the organic world metaphor in which the donor subject is a living being and the recipient subject is the universe. The verbal animation of the universe is not meant to be considered as a potential source of theoretically relevant insights: here, the organic metaphor is to be taken superficially, without theoretical implications of the kind which the clock metaphor, for example, had in the mechanist world theory. The similarities between the two subjects are not expected to be capable of being pushed further, beyond the ground of transfer: the non-appearance of changes. On closer inspection, the metaphor appears to be a clear instance of a "projection" rather than simply a "detection" of pre-existing similarity, as rendered in Black's interaction view of metaphor. The similarity of a dead organism and the cosmos in a state of thermal equilibrium results from the specific focusing accompanying their juxtaposition. The death of an organism means the ceasing of vital processes of this organism only, and not the disappearance of movement and changes. E.g. decay processes enter instead, and physical processes such as changes of temperature, movements caused by external forces, evaporation of fluids, etc., continue.

9.4. Maxwell's demon The concept known today under the name of "Maxwell's demon" came into existence in 1867, in a Gedankenexperiment devised by James Clerk Maxwell. Maxwell (1995: 332, in the letter to Tait from December llth, 1867) describes a vessel with two compartments divided by a diaphragm containing "elastic molecules in the state of agitation ..." He 413 414

Jeans 1930: 12-13. ibid.: 144.

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continues: Now conceive a finite being who knows the paths and velocities of all the molecules by simple inspection but who can do no work, except to open and close a hole in the diaphragm, by means of a slide without mass. Let him first observe the molecules in A and when he sees one coming the square of whose velocity is less than the mean square velocity molecules in B let him open the hole and let it go into B. Next let him watch for a molecule in B the square of whose velocity is greater than the mean square velocity in A and when it comes to the hole let him draw the slide and let it go into A, keeping the slide shut for all other molecules. Then ... the hot system has got hotter and the cold colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed.

Contemporary handbooks on thermodynamics frequently invoke Maxwell's invention retaining the personification, for example Zemansky and Dittman (1987: 299): Maxwell imagined a small creature stationed near a trap door ... The demon could not tell the difference between one kind of molecules and the other because he and the molecules are in an enclosure at a uniform temperature ... The demon could not see individual atoms.

The personified mode of referring to the "demon" is usually retained even if it is stressed that it is not to be taken at the face value: For historical interest, we would like to remark on a device invented by Maxwell ... He supposed the following situation: We have two boxes of gas at the same temperature, with a little hole between them. At the hole sits a little demon (who may be a machine of course!). There is a door on the hole ... He watches molecules coming from the left. Whenever he sees a fast molecule, he opens the door ... If we want ... he can have eyes at the back of his head, and do the opposite to the molecules from the other side ... It turns out ... that the demon himself gets so warm that he cannot see very well after a while ... Soon it is shaking from Brownian motion so much that it cannot tell whether it is coming or going ... so it does not work.415 (emphasis HP)

(Notice the sudden switch from "he" in the earlier lines to "it" in the last line, which, however, does not prevent the personification going on.) Bailyn (1994: 100, 178, 460) capitalises the first letter and writes of Maxwell's Demon it confirms the personification of the device, making its denotation look more like a proper name. The question arises whether the personified rendering of the "sorting device" was merely a matter of language or if it had some implications on the level of physical theory and concept formation. Maxwell's original presentation personified the demon verbally, but later

41

' Feynmanetal. 1965,1:46-5. "" "Concerning demons: 1. Who gave them this name? Thomson. 2. What were they by nature? Very small but lively beings incapable of doing work but able to open and shut valves which move without friction or inertia. 3. What was their chief end? To show that the 2nd Law of Thermodynamics has only a statistical certainty. 4. Is the production of an inequality their only occupation? No, for less intelligent demons can produce a difference in pressure as well as temperature by merely allowing all particles going in one direction while stopping all those going the other way. This reduces a demon to a valve. As such value him. Call him no more a demon but a valve like that of a hydraulic ram, I suppose." Maxwell, in Knott 1911: 214-215.

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he denied any commitment to the association between consciousness or intelligence and the sorting action conducted in his Gedankenexperiment, insisting on his preference for the word "valve" instead of "demon" and attributing the latter naming to Thomson416 (who, in turn, attributed it to Maxwell)417. Yet, we think that unlike "heat death" and "time arrow", the linguistic metaphor of "Maxwell's demon" became later, to some extent, the catalyst of such implications, marginal rather than essential, but not fully negligible - they are located at the interface between thermodynamics and information theory. Even if Maxwell's notion of the demon was a purely mechanical one, his "way of speaking" led eventually to the encounter of the notion of intelligence and thermodynamics. Maxwell calls his demon "intelligent". In view of his insistence, in the same paragraph, that it is to be thought of simply as a valve, it seems that he used a de-personified notion of intelligence, reducing it to automated behaviour, stimulusresponse chain with no implication of consciousness, humanity, and rational behaviour; this is also its contemporary meaning in Artificial Intelligence.418 Later, Thomson defined the demon as "an intelligent being endowed with free will", who "differs from living animals only in the extreme smallness and agility".419 Smoluchowski argued in 1913 that the original small demon could not be automated, but an intelligent creature could perform the action of the demon and operate a perpetual motion machine violating the second law. Finally, entropy became related to information by Szilard and Brillouin. Szilard identified the intelligence required of the demon as a kind of memory, and stated that a decrease in the entropy of a system must be preceded by the acquisition of information. This association was developed further by Brillouin who stated that "information is ... defined by the corresponding amount of negative entropy" (cf. Ehrenberg 1967: 100). It seems that we are entitled to interpret this association as a final result of the turn of thought facilitated, if not caused, by the verbal personification which from the very beginning accompanied the reflection upon the conditions in which the second law might be violated. The anthropomorphic notion of a demon facilitates the association of its action with consciousness and intellectual activity and the idea that the intellectual activity is the way to 'The definition of a demon, according to the use of this word by Maxwell ..." Thomson, William in Nature 9, 1874: 442.17 Schön 1963: 55. The founding father of AI, Norbert Wiener, was conscious of the semantic problem posed by the shared features of animated and automated beings. In 1954, he wrote: "Here I want to interject a semantic point ... Whenever we find a new phenomenon which partakes to some degree of the nature of those which we have already termed 'living phenomena', but does not conform to all the associated aspects which define the term "life", we are faced with the problem whether to enlarge the word 'life' so as to include them, or to define it in a more restictive way so as to exclude them ... The problem ... is, for our purposes, semantic and we are at liberty to answer it one way or the other as best suits our convenience ... When I compare the living organism with ... a machine, I do not for a moment mean that the specific physical, chemical, and spiritual processes of life as we ordinarily know it are the same as those of life-imitating machines. I mean simply that they both can exemplify locally anti-entropic processes ..." (pp. 31-32). This comment suits equally well Wiener's, Maxwell's and our own use of the word "intelligence" as it is applied to non-animated entities. Cf. Ehrenberg 1967, 103-110: 104, 105. On the other hand, Thomson called the conception of the sorting demon "purely mechanical". That means that for Thomson, the notion of intelligence and of mechanical functioning were semantically compatible, in the way we find them conjoined in the contemporary notion of Artificial Intelligence. His notion of free will is more question-begging, but the issue lies outside the scope of our subject.

213 reduce disorder, to produce a local decrease of entropy. This issue, as already recognised by Thomson, is beyond the scope of physics, but a valuable impulse for the appropriation of physical concepts by human sciences and literature. Among others, the demon appears in the works of Paul Valery and Thomas Pynchon. In Pynchon's "The crying of lot 49", the main character is asked by a weird amateur scientist to attempt to perform the function of the demon and sort slow and fast molecules by concentrating her attention upon a gas container with two compartments. The theme of the episode is the literalisation of the metaphor: the donor subject of "Maxwell's demon" is a creature, and Pynchon's physicists takes it literally, supposing that consciousness might actually be the relevant factor in the process in question. Valery draws upon the idea of human activity as a local decrease of entropy, and imaginatively transforms the demon into "an analogue for the relational and evaluative capacities of the human mind";420 he characterises the intellectual activity as a power similar to the achievement of "un demon ä la Maxwell".421 These examples illustrate how anthropomorphic wording may help create links between the scientific and the humanist discourses.

420 421

Crow 1972: 11. ibid.: 24.

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10. Transfer of denotations in the terminology of physics 10.1. Metaphors in general language and in the terminology of physics: the general language basis for the transfer of denotations The potential of a language for generating new lexical items is important for the growth of scientific language, and metaphor is a part of this potential. Production and comprehension of language comprise on the one hand a set of mental procedures used to couple a certain cognitive content with a corresponding linguistic expression, and on the other, the "stock" components in a given language. The language of physics selects its means from the general language from the sub-levels of lexicon, morphology (the morphological means for coinage of neologisms), syntax, and text grammar (cf. Godman and Payne 1981); we think that the "metaphorics" of a language should be added to these recognised levels as its distinct semantic and stylistic structural component. We claim that in the production of new items of physical terminology by transfer of denotations, not only are the same cognitive procedures utilised as in common language (such as e.g. juxtaposition, focusing, marginalising), but also the system of a natural language (in the example of English) contains a set of non-lexical semantic "stock" components which become utilised in the production of linguistic metaphors, and that the metaphorical transfer of denotations in physics also draws upon this stock of a given language. This "metaphorics" consists of underlying metaphors, frequent donor domains, violable restrictions and grounds of transfers established in a given language. It is essential for the production and comprehension of linguistic expressions in common language (including the non-terminological, "common language" part of scientific statements) as well as for creating scientific terminology. Metaphorical production is more difficult to account for than metaphorical comprehension. (This is why the studies of mental processes connected with the phenomenon of linguistic metaphor are almost exclusively confined to the analysis of comprehension.) The reason is obvious: whereas an already produced metaphor provides us with an (explicitly or implicitly) specified domain of the recipient and an (explicitly or implicitly) specified domain of the donor and the feasible task of specifying the ground of transfer, the metaphorical production involves finding a match for the denotatum among the options provided by the lexicon on the grounds left to the fantasy of the speaker. In some cases, the number of things similar in one or other respect to the recipient subject, that is, the number of the possible options for designation or expression of the intended meaning, seems limitless in principle. Koestler (1964) describes the cognitive process underlying the act of creation as a series of trial-and-error tests of the various combinations of possible concepts, claiming that "new ideas are thrown up spontaneously like mutations; the vast majority of them are useless, the equivalent of biological freaks without survival value". Similar proposals have been made to account for the nature of metaphor (cf., for example, Schön 1963). The account in terms of "random trial" can also be applied in explaining the process of extending scientific terminology by means of transfer of denotations, but we believe that the actual mental process taking place runs along a more efficient path. Certainly, creativity, which also includes analogical reasoning and linguistic creativity manifested in the production of metaphorical expressions and new lexical entries, cannot, by definition, be fully subsumed under a set of algorithms (recursive functions). The cognitive basis for the (re)cognition of similarity is multifaceted,

215 so it would be wrong to assume that we can exhaustively represent the process of metaphor production by any recursive function. However, we believe that such creative processes are not fully unguided. The search for the donor domain of the rules of conceptual manipulation in analogical problem solving, and also the search for fitting denotations for new concepts in science, are not completely random processes of trial and error. It is much more likely that they start with trying out a certain "standard" set of procedures with a high probability of success. We suppose that in his or her search for a suitable label, the seeker (a scientist) is assisted in this search by certain clues concerning where to look first, such as privileged grounds of transfer or domains which are likely to become donor domains of denotations. The speaker knows where to turn in search for the object of comparison, or which feature to replace conceptually in his concept by another (e.g.-human —> +human), in order to perceive it as similar to another object, which can thus become the donor of a denotation. This "priming" can be psychophysiologically or culturally grounded, and is reflected in general language. We argue that the metaphorical stock of general language constrains and directs the creation of new items of scientific terminology by metaphorical transfer. Among other things, in English and in other Indo-European languages, metaphorics includes: • hypostasis (nominalisation)

donor domain: thing, recipient domain: process, property, relation

• animism and anthropomorphism donor domain: living and human beings (violable semantic restriction: +human and/or +animate) - hylopsychism donor domain: psychic phenomena •synesthesis

donor domain: percepts of one sense, recipient domain: percepts of another sense

• spatialisation

donor domain: spatial relations

• shape similarity

ground of transfer: shape similarity between a recipient subject or its visual image and the donor subject

Apart from the more general "instructions for where to turn to in metaphorical production" listed above, a language puts at our disposal a set of particular underlying metaphors established conceptual relationships specifying more closely the donor and the recipient domain. Underlying metaphors are productive in all varieties of language. In the preceding chapters we exemplified the concept of underlying metaphor with instances such as more is up, important is central, processes are things, change is movement, things are men. In the terminology of physics, an underlying metaphor from the general language may find a more particularised realisation as an "underlying sub-metaphor" relating two more exactly specified domains: the synesthetic relation hearing is seeing from the general language is particularised as frequencies are colors in acoustics and electronics, where the transfer took place from vision via sound - acoustic waves - to frequencies of signals transmitting sound • radio waves - and, further, to frequencies of other electromagnetic waves. Instances of the lexicalisations of the relation "frequencies are colours" are pink noise, white noise, acoustic colouring, coloration of a sound.

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10.2. Types of transfer of denotations We initially enumerated the following kinds of transfer of denotations: A- fantasy metaphor; B- based on analogy of mathematical expression; C- based on scientific models and analogies; D- based on underlying metaphors of general language and cognition; E- stipulative catachresis based on isolated similarities. Fantasy metaphor appears abundantly in particle physics, where it has its own peculiar line of development, a clearly delineated history which we consider in detail. Metaphor based on the analogy of mathematical expression will be given a brief consideration and illustrated with a few examples rather than exhaustively examined. Transfer of denotations based on a scientific model has been dealt with in the section presenting the development of concepts of electricity. In what follows, we illustrate it further with another example, in which the donor subject of the analogical model belongs to a different scientific discipline (economic theory). At the same time, the metaphorical term we consider, "mechanical work", is an anthropomorphism displaying the tendency ubiquitous in thought and language to project human physiological, psychical, and social experience upon non-human and inanimate spheres, which has scientific as well as non-scientific manifestations. This example shows the interrelatedness between scientific analogies and underlying metaphors, and makes clear that the categories (C) and (D) above are accentuations in a continuum rather than exclusive compartments. We already dealt with spatialisation metaphors as instances of (D) where the transfer of denotations was inherently connected with the formation of theoretical concepts. In section 4.2., our objective was to point out the contribution of spatialisation metaphors to modelmaking and theory construction in general, and in order to achieve this we presented some linguistic metaphors generated jointly as elements of larger systems: of spatial models built upon underlying spatial metaphors. The examples of the latter sort were the band model of solids and the "geodetic-architectonic" model of the potential field surrounding an atomic nucleus. In what follows we present some further satellite metaphors of the spatial metaphors which perform the function of gap-filling in the technical vocabulary, and which are isolated rather than systematic. By this we mean that they are generated singularly and directly on the basis of an underlying metaphor rather than as elements of larger model-like systems. We recognise that the difference is of grade rather than of sort; a deeper analysis could possibly show that some of the items we name are not isolated but components of larger spatial models similar to the above-mentioned ones. Also other terms of metaphorical origin based seemingly on isolated similarities might turn out to be satellites of systematic underlying metaphors of everyday language if subjected to further analysis. We acknowledge that the border we could draw between (D) and (E) would be in many cases rather temporary and tentative. Therefore, instead of treating them separately in what follows, we choose rather to treat them jointly and to point out the existence of "underlying metaphors" where we have been able to detect them. In particular, animisms and anthropomorphisms in physical terminology illustrate the existence of a "grey zone" between (D) and (E): they are based on isolated similarities between the donor and the recipient subject, but, as argued before, at the same time they manifest the projection of

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human features upon non-human and inanimate spheres, prerequisite to the perception of these similarities.

10.3. The terminology of physics and related disciplines When discussing terminology of physics, it is not always possible to draw a demarcation line between it and the terminology of closely related engineering disciplines. The passage from theoretical and experimental physics through applied physics to the associated technical disciplines is fluid, the terminologies overlap (cf. Hoffman 1985). Nucleonics is both a branch of physics and an engineering discipline. The language of physics of semiconductors can hardly be separated from the language of technology of semiconductors. The laboratory of an experimental physicist deploys modern electronic devices, the names of which (of their parts, effects produced, etc.) appear in the accounts of the physical experiments, and whose functioning is often hardly separable from the processes to be observed (contrary to a situation when an electronic device is applied e.g. in the laboratory of a biologist where no such merger is conceivable), so that they may be regarded as belonging to the terminology of physics. In what follows, in the choice of terms taken into account we do not limit the field of "physics" too strictly, but we exclude metaphorical terms peculiar to the technes, such as names of technologies, devices employed in them, and their functions, constituting a vast class which would require a separate consideration.

10.4. Fantasy-metaphor: the case of particle physics In the past, new coinages enriching scientific terminology took their form from the morphological and semantic resources of the classical languages, by combining Greek or Latin roots and affixes. This translation method ensured that the new items would not be unduly familiar and blocked the importation of connotations from past usage, which suited the denotative intention of a scientist aiming to produce a non-ambiguous, one-to-one correspondence between a denotation and the object to be named. Nowadays, this method of producing new terms, although still used, is accompanied by a number of other strategies. Among them, the metaphoric transfer of denotations is especially frequent in those fields where new terms are produced with high frequency. The change in opinion concerning what is regarded as appropriate in terminology has been commented upon by Raad (1989: 129): Until recently, in order to describe an empirical world which appeared stable and permanent, the scientists adopted communicative devices (that is, terminology and norms of usage) which aimed to create a distance from emotive and suggestive variances in meaning. In other words, scientists attempted to remove their language from familiar associations ... Such a position is obviously not tenable in the world of science today. Nomenclature must remain controlled by the requirements of both uniformity and expressiveness, neither of which can in effect be subverted ... Recent changes in attitudes and in the nature of science and of language have created an environment where a shift is occurring in the perception of what is appropriate to meet the demands of expressiveness and intelligibility. While the earlier phases of science may have discouraged experimentation in nomenclature ... perhaps the international prestige of English today and the general liberalisation of attitudes have encouraged a new boldness in usage. Scientists are now more willing than before

218 to go public, and the new words of science are more likely to operate within linguistic framework of our ordinary speech, even to the extent of exhibiting emotive associations. We think that this new, liberal attitude to language is an expression of the changed metatheoretical predilections of physicists. In what follows we look at the language of particle physics as an arena of the most spectacular triumphs of metaphor as a means of enriching terminology. We will present the role of fantasy-metaphor in providing vocabulary for particle physics and reflect on the relationship between this linguistic phenomenon and the self-understanding of physics. The event decisive for the playful way of dealing with nomenclature in particle physics took place in 1964, when Murray Gell-Mann of the California Institute of Technology introduced the name quark to denote a theoretical entity in his model of elementary particles. This fantasy-name originates in Joyce's "Finnegan's Wake" and has no meaning in common language. As an act of coining a new scientific term, it was a rather revolutionary event because the linguistic label was assigned to the object to be named in a whimsical, arbitrary mode. It is to be noted that at the moment of the introduction of the quark model, quarks were not universally regarded as entities which could possibly be observed one day in a laboratory, but rather as theoretical constructs postulated to account of a set of experimental results: It is fun to speculate about the way quarks would behave if they were physical particles of finite mass (instead of purely mathematical entities as they would be in the limit of infinite mass). ... One of the quarks would be absolutely stable ... A search for stable quarks ... at the highest energy accelarators would help to reassure us of the non-existence of real quarks.422 Although "quark" is frequently referred to in a popular manner as "the" verbal metaphor in quantum physics, in fact it is no metaphor at all; its status is that of a pure neologism, as it has no meaning in any variety of English. Its importance for the metaphorical use of language in particle physics lies in its precedence-setting role. The introduction of "quark" was subsequently followed by the introduction of numerous whimsical and humorist items with which particle physicists named their theoretical objects. This process reflects a growing consciousness of the creative character of physical science, closely related to the fact that physical models are more and more distant from the world of direct experience which we referred to in the chapter on the linguistic views of contemporary scientists. In Klasson's formulation, today's scientists realise that they are up against something strange and unfamiliar; they are "like science fiction writers trying to convey something Utopian, unreal, to their readers".423 By that time one of the quantum numbers characterising elementary particles had been known for a decade as strangeness, and the particles characterised by a non-zero value of this number as strange particles. The motivation for this naming was the strangely long lifetimes of certain elementary particles for which the new quantum number provided a satisfactory account. Denoting a theoretical parameter by the name of a subjective impression it made on the researcher and the unquestioned acceptance it found among persons involved in the research was already a mark of the new, liberal approach to language. After Gell-Mann, in 1962, managed to gain acceptance for another denotation violating the traditional rules of scientific coinage, gluons, particles holding together the constituents of atomic nuclei,424 the 422 423

Gell-Mann 1964:215. Klassonl977:28.

219 path was prepared for even bolder linguistic events such as fantasy-names and fantasymetaphors. Quark quickly won popularity425 (gaining the upper hand over the rival label ace proposed by S. Zweig),426 and later in the same year, the term charm was introduced by Björken and Glashow (1964: 255) for their postulated additional quantum number of certain elementary particles. The next significant event in the vocabulary of particle physics came when Gell-Mann (1972: 736) introduced the term color to denote a proposed additional attribute (quantum number) of quarks. This attribute differentiated quarks into three types, which were assigned arbitrary names of three visual colours. By introducing this arbitrary property the concept of quark could be saved without violating Wolfgang Pauli's dictum that no two identical elementary particles can occupy the same place at the same time. The introduction of colors made quarks differ from each other and secured the preservation of Pauli's principle. Colors of quarks are unobservable: particles observable in laboratory experiments are supposed to be assemblies of quarks whose colors neutralise each other. The concept is saved by the additional assumption that only colorless particles are stable in nature.427 In Gell-Mann's original proposal, the colors of quarks were blue, red, white, and their anticolors anti-blue, anti-red, anti-white. These two triads of colors seem to still have been current in 1975.428 At present, the set of colors consists more frequently of blue, yellow, and red complemented by anti-red, anti-blue, and anti-yellow. (Occasionally, green is used instead of yellow; cf., for example, Nambu 1981: 116.) In scientific papers different colors are designated simply by letters which are not necessarily abbreviations of the linguistic labels,429 so that the latter usually appear only in introductory presentations of the concept of color. The colorless combinations of quarks are triads of yellow-blue-red and pairs which consist of a quark of a given color and an anti-quark of a complementary color. The later replacement of yellow for white in the set of colours labelling the three kinds of quarks was motivated by the fact that in time the colorless state had also come to be referred to as white*30 as well as by a desire for more systematicity: after this change the names of the colors of quarks corresponded to the names of the so-called primary additive colours. The force which keeps the quarks together which make up a particle (through the exchange of other elementary particles called gluons) came to be called as color force. The abstract mathematical space in which quarks may be "rotated" and thus made to change their colors, a "receptacle" of the colors of quarks, was given the name color space. We also speak today of color flux, and color current. The common language semantics of the concept of colour provides the guideline for the linguistic expression of further associated concepts, hence color transparency and color opacity (cf. Nikolaev 1994), opacity and transparency being concepts from the field of optical and visual phenomena. In the example of this extension we see how the introduction 424 425 426 427 428 429 430

Gell-Mann 1962: 1067.17 Schön 1963: 55. Used later in the same year by different authors, e.g. Greenberg 1964; Beg, Lee and Pais 1964. Zweig, in CERN Reports 8182/TH.401 and 8419/TH.412,1964. Both alternative names, quarks and aces, have been proposed in the article by Feynman, Gell-Mann and Zweig in 1964: 678. Whether this presumption has to be retained is presently a subject of further research. They appear e.g. in Physical Review Letters 34, No. 7, February 1975: 431, and No. 15, April 1975: 985. E.g. Physics Letters 60 B, No. 2, 1976: 178 where colored quarks are designated P, N, L. E.g. Nambu 1981: 117: "All hadrons are in 'colorless' or 'white' state."

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of one metaphorical term may be followed by the development of a network of terms whose labels are taken from the same donor field. This way stipulative catachresis including fantasymetaphor may perform a linguistically similar function as an analogical model, the function to which Martin and Harre (1982) referred as "spinning off a matrix of terminology" (cf. section 2.4.3.). A linguistically interesting achievement of particle physics was the introduction, by analogy with the earlier theory known as quantum electrodynamics, of the term quantum chromodynamics,431 to denote the branch of physics dealing with colors of quarks and the color force. It applies the traditional method of coining new terms by drawing upon a set of ancient morphemes, but one of these morphemes is a product of the translation into Greek of a highly whimsical modern metaphor. Another option for combining the traditional method with the existing metaphorical labels is by affixing a vernacular morpheme with a classical affix. In 1975, the terms charmonium, orthocharmonium and paracharmonium were introduced by Appelquist and Politzer (1975: 45) to name particles consisting of a charmed quark-antiquark pair. Other new coinages of the same type followed: Some more applications of QED wave also made to decays of heavy quarkonia such as J/y 's (charmonium) and g's (bottomium) and to nonleptonic decays of hadrons.4" (emphasis HP) In so far as these terms may be conceived of as a reflection of the self-understanding of physics, we can see them as an encounter in one word of the pretence of science for authority and seriousness and the playful attitude which is conscious of its constructive, creative character. The transfer of denotation from the visual quality (colour) to the hypothetical theoretical property of quarks is usually regarded as a pure fantasy-metaphor: catachresis in which a name is transferred to a new sort of referent on arbitrary choice, but there are some grounds which make it possible to group it with the more usual sort of catachresis motivated by a certain amount of similarity or analogy between the donor and recipient subject. The analogy between the properties of quarks and the colours of concrete objects is weak and an afterthought, but not altogether non-existent, and it has been sometimes indicated as the motivation for the transfer. According to Johnson (1979: 103), The word color is used because the way different colored quarks combine is reminiscent of the way visual colors combine. If we assume that the transfer of denotation was actually based on an analogy rather than fully whimsical, its ground may be described as follows: coming in combinations, particular colors of quarks (or, more precisely, colored quarks) are not observable, just as in a mixture of visual colours the component colours are not observable. Quarks of a given color combine into colorless assemblies with antiquarks of the complementary anticolor, just as the socalled complementary (visual) colours additively mixed provide mixtures which are perceived as colourless. The analogy is weak because the combinations of primary additive colours (red, blue, and yellow) do not produce a "white", or colourless, mixture: the basic character of primary additive colours lies in the fact that all other colours can be produced

451 452

Attributed to Gell-Mann. The primary written source could not be identified; the term originated possibly in oral communication. Muta 1987: 4.

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by their combination. Moreover, as previously indicated, at the time of the introduction of the term color, the proposed namings of the particular colors did not correspond to the primary additive colours; a rather casual set was proposed at first, to be systematised later by the replacement of white by yellow. MacCormac (1985: 223) states that using colors as labels for properties of quarks contributes to the researcher's tendency to think of quarks as definite objects. It remains difficult to conceive of things as colored (even if color is attributed to them on an analogical basis) without also conceiving of them as finite, definite, and available.

While agreeing with his point that naming a hypothetical property of quarks "color" enhances to a certain degree the imagistic aspect of their mental representation, we think that denoting abstract attributes by largely arbitrarily assigned names of sensorial attributes also has a contrary aspect. The obviously fanciful character of this naming also expresses the reservation on the part of the researcher that the theoretical description is not to be taken at face value, as a literal one. Just as color is not to be interpreted as what it usually means, i.e. a sensory quality of definite, finite, available entities, so its carriers - quarks - are not to be interpreted as such entities. To some extent, the statement that "quarks are colored" through a "literal falsity" of the predication points to the "as-if" character of quarks as the presupposed subject of the predication. The following text seems to us to support this view; it is a fragment of the first publication in which the term "color" was used by the author of both coinages Gell-Mann: We take three different kinds of quarks, that is nine altogether, and call the new variable distinguishing the sets 'color', for example red, white and blue (R-W-B) ... We require that all physical baryon and meson states be singlets under the SU3 of 'color' ... This restriction to color singlet states for real physical situations gives back exactly the sort of statistics we want. Now if this restriction is applied to all real baryons and mesons, then the quarks presumably cannot be real particles. Nowhere have I said up to now that quarks have to be real particles. There might be real quarks, but nowhere in the theoretical ideas that we are going to discuss is there any insistence that they be real. The whole idea is that hadrons act as if they are made up of quarks, but the quarks do not have to be real.4" (emphasis HP)

Around 1975, another sensory quality lent its label to the nomenclature of particle physics:

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Gell-Mann 1972: 736-737. The comments on quarks being or not being "real" physical entities sound curious when juxtaposed with the assertions of Heisenberg, Bohr, Born, etc, quoted earlier in this work, which pictured the whole of particle physics as an "as-if" theoretical construct. The sense in which elementary particles like e.g. electron (once a wave, once a particle) are more "real" than other theoretical entities called quarks is not self-evident in the light of what has been said about the nature of scientific theorising in the world of atomic and subatomic dimensions. One way to explain away this inconstistency is by attributing different degrees of "scientific realism" to particular researchers involved in the process of knowledge growth. We accept this "psychological" explanation as a satisfactory kind of answer without plunging into a reconstruction of the discussion which has taken place with particular intensity in the philosophy of science in the last few decades concerning the way in which observable experimental results are interpreted and bound to theoretical concepts. At this point, it is sufficient to refer to what has been said in this context about the relation between metaphorical processes and scientific theorising in section 2. 3.

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flavour.™ In order to account for conservation of the quantum numbers in hadronic reactions one assumes the existence of different kinds of quarks corresponding to these conserved quantum numbers; flavor is the generic term for the set of quantum numbers, that is, of the types of quarks. Just as the colors of quarks can be changed by rotating them in color space, so a quark of one flavor may be turned into a quark of another flavor by rotation in a flavor space conceived as a receptacle of flavor of quarks. Two opposite flavors (e.g. of a particle and its antiparticle) cancel out each other and a particle consisting of quarks of opposite flavors is said to be flavorless. The introduction of strangeness and charm as terms referring to quantum numbers and quarks was followed by the proposal by Achiman, Koller and Walsh (1975: 261) of another type of quark which they called fancy, but the concept, and the associated term, has not gained ground. Also in the same year, another group proposed a new quantum number gentleness*** (quarks displaying this property were called gentle), but this concept, too, has not found enough support and the new term has failed to enter the lexicon. The same thing happened to the independently proposed term justice (cf. Gregory 1988)436. The arbitrary spatial terms up and down, distinguishing between two possible values of the quantum number called isotopic spin, were introduced by Gell-Mann (1964: 219)437 along with strange as names for three kinds of quark. ("Strange" quark is the one responsible for the earlier mentioned "strangeness" of "strange particles".) Top and bottom were added to the flavor family by Harari (1975: 265) who proposed a group of top, bottom, and right quarks besides the existing group of up, down, and strange ones. The three terms came from the visual representation of their configuration in an abstract two-dimensional space. Top and bottom referred again to the values of isotopic spin, represented by the vertical axis in the representation, higher for the top quark and lower for the bottom quark. The term "right" has not survived.438 The customary abbreviation of top and bottom quarks with their initial letters, resulting in

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435 436 437 438

The source publication could not be identified, but flavor is missing from publications before 1975 and frequently used in 1976. The invention of the term flavor is usually attributed to Y. Nambu, but he himself comments: "Frankly I do not know why and when people started to attribute the term 'flavor' to me ... Once (or more than once) 1 heard that Gell-Mann had attributed the term 'color' to me. He himself may have said so to me. But that is definitely not accurate. I started the concept, not the name ... May be the case of flavor is similar. In the seventies when QCD and color became popular, I heard that Glashow was using the term flavor, though I did not know for what exactly. Then I also talked to someone over the telephone about the name flavor in the context used now. I thought I was quoting him. But I may have been misinterpreting what I had heard." In a letter to the author from 18. July 1996. Mentioned in ScAm, May 1975: 43; the original source could not be identified. Mentioned by Gregory 1988. Gell-Mann used the abbreviations u, d, and s for "strange". Today, the standard model in particle physics is based on the assumption that ordinary matter is composed of two kinds of particles, quarks and leptons, and that the forces between them are transmitted by a third category of particles called bosons. Quarks come in three families, each of them consisting of two particles: the first family consists of the up and the down quark; the second consists of the strange quark embodying the flavor called strangeness and the charmed quark embodying the flavor called charm; the third family of the bottom quark and the (predicted but so far not experimentally supported) top quark, embodying respectively flavors of the same names, termed alternatively beauty and truth.

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talking of e.g. "bb quark system" and "b-flavored mesons",439 gave rise to another fanciful linguistic innovation: the bottom quantum number embodied by the bottom quark and the quantum number embodied by the hypothetical top quark are occasionally renamed as beauty and truth. Beauty was at first a "hidden" property of quarks making up some observed products of subatomic collisions. In the early eighties, Mistry, Poling and Thorndike announced that they had succeeded in creating particles in which this flavor was no longer hidden; they declared it to be naked and proclaimed (1983: 104) that their newly created particles displayed "naked beauty (or bare bottom)".440 It is to be noted that beauty and truth belong to the type called luxury metaphors (or luxury terms) because the alternative, syntactically equivalent terms top and bottom existed already and the new terms were redundant for all but decorative purposes. They are mainly applied in popular scientific texts and were probably introduced in this context. E.g. the composed particles exhibiting the flavor of beauty (such as mesons made of two quarks, one of which is endowed with beauty) are called b-flavored in scientific texts and beauty-flavored in corresponding popular texts.440 This points to the fact that the fantasy terms in physical terminology gradually acquired one more function, that of representing physics for the layman in an attractive, attentioncatching and stimulating wrapping. The fancy-labels share this function with such imagistic shorthand-paraphrases as Maxwell's demon, heat death, arrow of time, the difference lying in the degree to which the adoption of a given word to express a given notion is motivated by its semantics. In the 17th century, philosophers set a cornerstone of modern physical science in introducing a distinction between secondary and primary qualities. The ultimate theoretical description of the physical world, and of the secondary qualities themselves as the products of the action of external reality upon human senses, was to be given in terms of primary qualities. Qualities other than the primary (i.e., other than number, figure, magnitude, position, and motion), although often prominent to the senses, came to be regarded as secondary, subordinate effects of the primary. For Galileo as well as for Descartes, they were also the effect of the senses themselves. They were regarded as confusing and untrustworthy elements in the sense-picture of nature, with the following effect: Till the time of Galileo it has always been taken for granted that man and nature were both integral parts of the larger whole, in which man's place was the more fundamental. Whatever distinctions might be made between being and non-being, between primary and secondary, man was regarded as fundamentally allied with the positive and the primary ... Now, in the course of translating this distinction of primary and secondary into terms suited to the new mathematical interpretation of nature, we have the first stage of reading of man quite out of the real and primary realm.*41 The meta-theoretical predilections associated with this programme have been abandoned in the meantime, and the change in the self-understanding of physical science finds expression in a playful return to secondary qualities as a source of idiom. Color, flavor, and the spatial terms up and down, bottom and top, naming originally directly observable attributes, have become successful as items of terminology. In the search for new labels, the physicists have turned not only to the domain of sensory attributes ("secondary qualities") but also to the sphere of human judgements and emotions, with names such as charm, gentleness, justice, 4511 440 441

Physical Review Letters 45, 1980: 221. E.g. Physical Review Letters 45, 1980: 221 versus ScAm, July 1983: 99. Burtt 1924, 1967: 78-79.

224 beauty, or truth, pertaining originally to human aesthetic and moral judgements. As it became clear that the language of physics could not be purified from the metaphorical component because we are condemned to use, in a physical description, a language which has grown in communication about ordinary experience and is not convergent with the insights of modern science, physicists have turned the vice into a virtue and engaged in a playful enterprise of linguistic inventiveness.

10.5. "Mechanical work": underlying metaphor, world theory, scientific analogy As a physical term, "work" is presently defined as the transfer of energy to a physical system. The origins of the concept of work date back to the end of the 18th century, when James Watt introduced a measure for the efficiency of machines. Prior to his proposal, the performance of various sorts of machines could not be quantitatively compared. Watt defined the power of one mechanical horse as the ratio of the product of the weight of an object times the height to which it has been lifted, generalised as force times distance, to the time required for the lifting of this object. Because of its usefulness in comparing efficiency of mechanical devices, since the end of the eighteenth century the concept of weight times height has achieved a growing importance in technical mechanics. The first case of defining weight times height as a separate physical value was Carnot's "Essai sur les machines en general" (1782). Carnot named it "force vive latente" or "moment d'activite". In the following decades this quantity, referred to with different names, received a primary importance in the works of French physicists dealing with technical mechanics. Mechanical work became a central concept of this discipline. In physics, the notion of work began to play an important role after the formulation of the principle of conservation of energy, indebted for its birth to the perception of all natural processes through the prism of the working machine performing the kind of physical action prototypical in the new scheme of thought - displacing heavy objects against resisting forces. In 1826, Coriolis and Poncelet used the name "travail" for the first time. The term was first translated from French into English as "labouring force" by William Wheewell (1841). Several concepts exposed in the preceding parts intercept in the transfer of denotation from work as human activity to mechanical work: anthropomorphism as an underlying metaphor, mechanism as a world theory, scientific analogy. At first glance a simple anthropomorphism, if analysed within its intellectual and social context, the transfer of "work" as a denotation for the activity of machines (later extended, via mechanism, to all kinds of physical systems), turns out to display the opposite tendency - MacCormac's "mechanification" (see page 166). After the industrial revolution, human work became dissociated from its social aspects and measurable in terms of the same operations of which machines are capable. This change of perspective created conditions in which the word "work" could be applied to designate a mechanical concept expressing a mathematical relation offeree and distance: Whewell's use of the term 'labouring force' expressed his parallel interests in the science of political economy and its labour theory of value. 'Labouring force is the force we pay for', Whewell explained, and went on to develop the economic theory distinguishing work done by machines (equivalent to the wages of labour) from work accumulated in storehouses such as reservoirs of water or

225 flywheels (equivalent to capital).442

The transfer of denotation from the activity of men to the activity of mechanical systems was, then, supported by an analogy linking economical and physical theory. The image of the working machine replacing human workers, which made possible the transfer of the word "work" to denote an aspect of the functioning of machines, is part and parcel of the world picture in which economy establishes itself as an independent theoretical discipline, work becomes dissociated from human values and changes from a social activity into the process of production in which machines and men are interchangeable, and human workers are one of the available natural resources.

10.6. Catachresis and satellite metaphors What follows is a list of terms of metaphorical origin, sorted according to principles of transfer, donor domains, or both. Our collection comprises metaphorical expressions • lexicalised in the terminology of a given specialist's language, e.g. particular disciplines and sub-disciplines of physics; • lexicalised first in the specialist's language and generalised in everyday language (e.g. "spectrum", originally meaning a ghost); • lexicalised already in everyday language and taken over into terminology with a more precise meaning extrapolated from the meaning in everyday language (e.g. "band" for range in everyday language -* "waveband"). We describe briefly the semantics of the transfer specifying the relevant aspect of the meaning of the donor subject and the ground of transfer.443 Our collection is considerably broader than any of those we have come across in works on scientific and physical terminology including 442

Smith 1990: 329-330. **' This description could be done in a formalised or a semi-formalised mode, involving a componential analysis of the meaning of the donor subject. For example, in order to describe the semantic structure of "trap", we could try to atomise its meaning in terms of elementary functional components recurring throughout language - such as "target", "goal", "instrument", etc., in accordance with the "atomist", reductionist approach to meaning. This would result in something like the following: TRAP: TARGET: prevent (go GOAL) GOAL: want (implies) +volition GOAL (implies) +animate GOAL

(go GOAL) (implies) +movable GOAL

Or, in another type of formalised representation: TRAP: (Y prevents (leaves, X)) and (+animate, X) and (- agree, X) and (+ surprised, X) and (- happy, X)... We do not attempt to deploy any such kind of formalism or semi-formalism because in view of our notion of meaning such proposals seem to us to be rather arbitrary and misplaced outside AI research and applied linguistics, and we do not think that any cognitive gain could be achieved by such means compared to a description in natural language.

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sections on metaphorical terms, and might serve as a point of entry for a more thorough treatment of transfer of denotations in physical terminology than the one we are able to offer here. It is sometimes argued that word meanings come about by restricting more general meanings rather than generalising more specific meanings. In this case, one might argue, some expressions which we classify as metaphorical should be properly regarded as nonmetaphorical because their new referents show the more general property which originally defined them. We agree that the restriction and expansion of meaning may take place successively, sometimes in a recursive manner, but we apply the notion of metaphor to the expansion of meaning of an expression compared with the dominant use of it at a given time, whatever it might be at earlier stages. The terms listed below are mainly multi-word terms, which are commonly used to represent the growing stock of concepts. We list them in alphabetical order, referring first to the metaphorical item within the multi-word term and secondly to the other component(s). 10.6.1. Miscellaneous spatial metaphors In what follows we differentiate between the categories of spatial metaphor and metaphor based on similarity in shape or size, but we recognise that they cannot be sharply distinguished. There are clear-cut cases and border-line cases where classification becomes difficult. Cases of metaphor evidently based on shape similarity are those where both the donor and the recipient subjects of a denotation are concrete objects, like a train or a sawtooth on the one hand, a kind of crystal or a fragment of a graphical representation on the other. Frequently, however, we are concerned with recipient subjects which are not concrete objects but abstract concepts, like causal sequences or processes. Their denotation with names stemming from concrete objects depends on their spatialised, visualised conceptualisation. We classify them with metaphors based on shape similarity rather than with spatial metaphors if the spatial conceptualisations they express seem to be singular and specific to them; that is, if we are not able to reduce them to one of more general, common underlying spatial metaphors, such as MORE IS UP, RANGES ARE REGIONS, STATES ARE CONTAINERS, AMOUNTS ARE POINTS ON A SCALE, CHANGE IS MOVEMENT, or to trace them back to a nonvisual spatial experience motivating the transfer (as in the case of high and low sounds and accoustical volume). The donor subjects of such shape metaphors are concrete objects of material existence (such as chain or envelope) rather than abstract geometrical objects (such as point or region). Below is a collection of terms generated from underlying spatial metaphors. The conceptual line from the metaphor to a given denotation is briefly outlined. band=bandwidth:

1. A range of frequencies, usually specifying the number of hertz of the band or the upper and lower limiting frequencies. 2. The range of frequencies that a device is capable of generating, handling, passing, or allowing, usually the range of frequencies in which the responsivity is not reduced greater than 3 dB from the maximum response.444

Fiber Optics and Lightwave communications. Standard dictionary. 1981.

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pass-band=passband:

the frequency range within which a band-pass filter transmits without appreciable attenuation.44' That part of a filter which allows transmission of the signal; the frequency bandwidth of the transmission.446

sideband:

the frequency band on either side of the carrier frequency within which fall the frequencies of the waves produced by modulation. The term is also applied to the wave components lying within such a band. "5

side

frequency:

any frequency of a sideband.447

The underlying metaphorical relation is RANGES ARE EXTENDED OBJECTS. Ranges of wavelengths or energies are extended objects, having central portions and peripheries or sides; the extremes of the values of wavelengths or energies are the edges or boundaries of these objects.

waveband:

range of wavelengths occupied by transmission of a particular type, e.g., the medium waveband (from 200 to 550 metres) used for broadcasting. *"

The underlying metaphorical relation is RANGES ARE EXTENDED OBJECTS. band edge absorption:

in optical fiber glass, absorption that occurs in the visible region that extends from the ultraviolet region of the spectrum.444

The underlying metaphorical relation is RANGES ARE EXTENDED OBJECTS. Ranges of wavelengths or energies are extended objects, having central portions and peripheries or sides; the extremes of the values of wavelengths or energies are the edges or boundaries of these objects. band-spreading:

use of a relatively large fixed capacitor in parallel with a smaller variable capacitor, to reduce the band of frequencies covered by the variation of the latter. *"

The term is based on the conceptualisation of ranges of frequencies as extended elastic physical objects. In order to reduce the distances in the vertical direction they are spread horizontally, becoming flatter. sound barrier:

the magnitude of the velocity of sound, which has to be exceeded before a projectile can be considered supersonic, i. e. having the Mach number greater than 1. ***

boundary wavelength:

in a continuous X-ray spectrum: the shortest wavelength quantum limit present. *"

The underlying metaphorical relation is RANGES ARE EXTENDED OBJECTS. Ranges of wavelengths or energies are extended objects, having central portions and peripheries or sides; the extremes of the values of wavelengths or energies are the edges or boundaries of these objects.

445 446 447

Concise Dictionary of Physics. 1979. Sound (=International Dictionaries of Science and Technology). 1975. Dictionary of Electronics and Nucleonics. 1969.

228 channel:

(1) General term for a unique transmission path. (3) Range of radio frequencies occupied by a modulated transmission ... A clear channel is one occupied by a single transmission, free from interference from other transmissions. *"

A channel is the bed where a natural stream of water flows; or a narrow region of sea between two land masses; or a usually tubular enclosed passage, especially for liquids. Extended to a "path" along which a signal "passes". As a physical term of the meaning defined above, it is similar to "band" in denoting a range of frequencies. closed shell:

of electrons in an atom or a molecule: characterizes a system in which all the quantum states of a particular shell are filled.445

closed/open system:

a system not allowing/allowing the exchange of energy or matter or information with other systems, respectively.

"Closed" means separated from outside with continuous borders not easily penetrable by things or influences. It is metaphorically transferred to systems of things allowing no influences from sources not part of these systems already in common language. Systems are conceptualised as having "inside" and "outside": components of the systems are "inside" the system and all other things are "outside". luminance range compression:

in lightwave, facsimile, or photoelectric transmission systems, a reduction in the luminance range of the signals in the transmission medium or in the display image from the luminance range of the object. *44

The underlying metaphorical conceptualisation renders RANGES of values of physical quantities as EXTENDED ELASTIC OBJECTS capable of being compressed or stretched. Quantitative differences are conceptualised as distances in space. condensed system:

a substance or mixture of substances in the liquid or solid state. The term has also been applied to the condensation into a state of zero momentum of the particles of an ideal gas obeying Bose-Einstein statistics.448

Bose-Einstein condensation:

for a vapour to the molecules of which Bose-Einstein statistics apply: the condensation of the vapour to a state in which some of the molecules have a momentum of nearly zero instead of having their momenta spread over a large range of values. 445

The underlying metaphorical relation is STATES ARE CONTAINERS. Energy (momentum) states contain particles; if there are a large number of particles in a given energy state, they are densely packed. deep sound:

low in pitch, as of a bass voice or any sound in a similar frequency range.44